Chain Rule Study Resources

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  • MAT 267- Exam 2 Practice Questions with answers

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  MAT 267- Exam 2 Practice Questions with answers

  School: Arizona State University

  Course: MAT 267

  ... Test 2 Solutions 1) Use the chain rule to find ∂z ∂s if z = exy, x = 7s + 8t, y = st4. Applying the chain rule, we have ∂z ...

• 3 Pages

  • Exam2Type1Sol

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  Exam2Type1Sol

  School: San Diego State University

  Course: MATH 252

  ... 1. We have d dx F (x, y (x)) = 0 for each x ∈ J. By the chain rule, 0 = d dx F (x, y (x)) = dF (x, y) dx + dF (x, y) dy dy dx Therefore, dy dx= − ...

• 5 Pages

  • Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

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  Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

  School: New York University

  Course: MATH 211.001

  ... Calculate the marginal revenue when q = 10. Solution: The marginal revenue, MR, is obtained by differentiating the total revenue function, R. We use the chain rule so MR = dR dq = 1 1 + 1000q2 · d dq (1000q2) = 1 1 + 1000q2 · 2000q. ...

• 1 Page

  • Assignment 4 Chain rule

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  Assignment 4 Chain rule

  School: University Of Waterloo

  Course: MATH 237

  MATH 237 ASSIGNMENT 4: Chain Rule Winter 2015 Submit your work at ... 1. Let w = x2y + xy3,x = 3t + 5,y = 2t2 - 10. Use the chain rule to calculate dw dt when t = -2. 2. Write the chain ...

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• 3 Pages

  • 4.3_Notes

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  4.3_Notes

  School: University Of Washington, Tacoma

  Course: MATH 126

• 2 Pages

  • Math 1A Review Worksheet

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  Math 1A Review Worksheet

  School: University Of California, Berkeley

  Course: MATH 54

• 2 Pages

  • Review of Calculus 1

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  Review of Calculus 1

  School: University Of Toronto

  Course: MAT 235

• 2 Pages

  • 5.3_Notes

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  5.3_Notes

  School: University Of Washington, Tacoma

  Course: MATH 126

Chain Rule Homework Help View All Chain Rule Study Resources Homework Help

• 5 Pages

  • Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

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  Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

  School: New York University

  Course: MATH 211.001

  ... Calculate the marginal revenue when q = 10. Solution: The marginal revenue, MR, is obtained by differentiating the total revenue function, R. We use the chain rule so MR = dR dq = 1 1 + 1000q2 · d dq (1000q2) = 1 1 + 1000q2 · 2000q. ...

• 1 Page

  • Assignment 4 Chain rule

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  Assignment 4 Chain rule

  School: University Of Waterloo

  Course: MATH 237

  MATH 237 ASSIGNMENT 4: Chain Rule Winter 2015 Submit your work at ... 1. Let w = x2y + xy3,x = 3t + 5,y = 2t2 - 10. Use the chain rule to calculate dw dt when t = -2. 2. Write the chain ...

• 3 Pages

  • MATH 204 Fall 2007 Assignment 3 Solutions

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  MATH 204 Fall 2007 Assignment 3 Solutions

  School: McGill University

  Course: MATH 204

  MATH 204 - SOLUTIONS 3 1. (a) The derivative can be obtained using the chain rule; the derivative of the term (yi − β0 − β1xi)2 with respect to β0 is 2 × (yi − β0 − β1xi) × (−1) = −2(yi − β0 − β1xi) ...

• 4 Pages

  • Homework 4

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  Homework 4

  School: University Of Toronto, Mississauga

  Course: MATH 21aY

  Math 21a: Multivariable calculus Homework 4: Chain Rule This homework is due Wednesday, 10/16 rsp Tuesday 10/15. 1 [Compare Stewart 11.5: 2 ] Use the chain rule to find the derivative dz/dt for z = cos(x + 7y) , ...

Chain Rule Lab Reports View All Chain Rule Study Resources Lab Reports

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  • Nicholas Terrones Week 2 Lab Page 4 GRADED 1 - 23 - 16 DR

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  Nicholas Terrones Week 2 Lab Page 4 GRADED 1 - 23 - 16 DR

  School: DeVry University, Chicago

  Course: MATH 260

  Category 4: Chain Rule ... 6.) Describe, in your own words, how to find the derivative using the Chain Rule, then find the ...

• 2 Pages

  • MA103_W14_wk6solns

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  MA103_W14_wk6solns

  School: Wilfred Laurier University

  Course: MA 103

  MA103 Week 6 Report - Chain Rule; Implicit Differentiation; Logarithms Name: Student Number: Lab Winter 2014 ...

• 8 Pages

  • M137-week5

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  M137-week5

  School: University Of Waterloo

  Course: MATH 137

  ... 1. Chain Rule revisited Chain Rule. [f(g(x))] = f (g(x)) · g (x) Remark. In Leibniz notation, if y = f(u) with u = g(x), then Chain Rule says ...

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  • MTH-240-Lab12

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  MTH-240-Lab12

  School: Ryerson University

  Course: MTH MTH240

  Ryerson University Lab 12 - MTH 240 1. Problem 7 Section 14.5 Use the chain rule to nd z/s and z/t. z = x2 y 3 , x = s cot t, y = s sin t 2. Problem 21 Section 14.5 Use the chain rule to nd z/s, z/t and z/u when s = 4, t = 2, u = 1. z = x4 + x2 y ...

Chain Rule Notes View All Chain Rule Study Resources Notes

• 4 Pages

  • exam2solutions

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  exam2solutions

  School: University Of Georgia

  Course: MATH 2250

  Math 2250 Exam #2 Solutions 1. Find the derivatives of the following functions. (a) f(x) = ln(tan−1 x) Answer: Using the Chain Rule, f (x) = 1 tan−1 x d dx (tan−1 x) Remembering that the derivative of tan−1 x is 1 1+x2 , the above becomes ...

• 2 Pages

  • lab3_f11

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  lab3_f11

  School: University Of Waterloo

  Course: MATH 116

  Math 116 - Lab 3 - Fall 2011. Rules for differentiation, chain rule, derivatives of trig, exponential, hyperbolic, inverse trig and inverse hyperbolic functions (Sections 3.3, 3.5-3.7 of L/G). You are to provide full solutions to the following pro...

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  • 265Lesson11Problems(3)

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  265Lesson11Problems(3)

  School: University Of North Dakota

  Course: MATH 265

  MATH 265: MULTIVARIABLE CALCULUS: LESSON 11 PROBLEMS Problems are worth 20 points each. (1) Let f(u, v) = u + v + uv2 and u = u(x, y) = ex + y, v = v(x, y) = xy. Use the Chain Rule to compute ∂f ∂x and ∂f ∂y . (2) Repeat problem 1, but thi...

• 12 Pages

  • Practice2S

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  Practice2S

  School: University Of Illinois, Urbana Champaign

  Course: MATH 231E

  Math 231E. Fall 2013. Midterm 2 Practice Solutions. Problem 1. Compute the derivatives of the following functions a. f(x) = cos(x2)esin(x) b. f(x) = arctan(x) c. f(x) = ln(ex(1 + x2 + x3)) Solution: a. We use the product and chain rules. We have d...

Chain Rule Test Prep View All Chain Rule Study Resources Test Prep

• 3 Pages

  • MAT 267- Exam 2 Practice Questions with answers

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  MAT 267- Exam 2 Practice Questions with answers

  School: Arizona State University

  Course: MAT 267

  ... Test 2 Solutions 1) Use the chain rule to find ∂z ∂s if z = exy, x = 7s + 8t, y = st4. Applying the chain rule, we have ∂z ...

• 3 Pages

  • Exam2Type1Sol

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  Exam2Type1Sol

  School: San Diego State University

  Course: MATH 252

  ... 1. We have d dx F (x, y (x)) = 0 for each x ∈ J. By the chain rule, 0 = d dx F (x, y (x)) = dF (x, y) dx + dF (x, y) dy dy dx Therefore, dy dx= − ...

• 19 Pages

  • Final Exam Study Guide on Calculus II

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  Final Exam Study Guide on Calculus II

  School: University Of Illinois, Chicago

  Course: MATH 181

  ... 1. Differentiate the function: F(x) = ∫ x2 √x et3 dt Solution: Using the Fundamental Theorem of Calculus Part II and the Chain Rule, the derivative of F(x) = ∫ h(x) g(x) f(t) dt is: F′(x) = d dx ∫ h(x) g(x) f(t) dt ...

• 2 Pages

  • Chain Rule HW 2

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  Chain Rule HW 2

  School: Estrella Mountain Community College

  Course: MAT 220

  MAT 220 CHAIN RULE HOMEWORK 2: TRIGONOMETRIC DERIVATIVES Determine the derivative of each function. ...

Most Recent Chain Rule Documents Uploaded

• 3 Pages

  • 4.3_Notes

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  4.3_Notes

  School: University Of Washington, Tacoma

  Course: MATH 126

• 2 Pages

  • Math 1A Review Worksheet

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  Math 1A Review Worksheet

  School: University Of California, Berkeley

  Course: MATH 54

• 2 Pages

  • Review of Calculus 1

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  Review of Calculus 1

  School: University Of Toronto

  Course: MAT 235

• 2 Pages

  • 5.3_Notes

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  5.3_Notes

  School: University Of Washington, Tacoma

  Course: MATH 126

• 2 Pages

  • lecture 2M

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  lecture 2M

  School: University Of California, Santa Barbara

  Course: MATH 118c

• 2 Pages

  • lecture 1F

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  lecture 1F

  School: University Of California, Santa Barbara

  Course: MATH 118c

• 1 Page

  • Section 5.5 Warmup

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  Section 5.5 Warmup

  School: Montgomery College

  Course: MATH 182

• 5 Pages

  • Lec17_ChainRule

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  Lec17_ChainRule

  School: Virginia Tech

  Course: MATH 1225

• 6 Pages

  • Lec16_ChainRule

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  Lec16_ChainRule

  School: Virginia Tech

  Course: MATH 1225

• 18 Pages

  • 8.Integration

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  8.Integration

  School: National University Of Singapore

  Course: MATH 1013

• 30 Pages

  • Lecture04复合函数的微分_848006034

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  Lecture04复合函数的微分_848006034

  School: Tsinghua University

  Course: MATH 973

• 5 Pages

  • Section-3.4

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  Section-3.4

  School: Virginia Tech

  Course: MATH 1205

• 4 Pages

  • 3.7

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  3.7

  School: University Of Colorado, Denver

  Course: MATH 1401

• 3 Pages

  • 11.5 Lecture Notes

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  11.5 Lecture Notes

  School: Dalhousie University

  Course: MATH 1115

• 7 Pages

  • Week3

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  Week3

  School: University Of Victoria

  Course: MATH 122

• 6 Pages

  • MATH%20207%20Fall%202016%20Solution%204

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  MATH%20207%20Fall%202016%20Solution%204

  School: University Of Waterloo

  Course: MATH 207

Chain Rule Homework Help

• 5 Pages

  • Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

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  Math for Econ I- Practice Problems New York University 5. Product, Quotient, and Chain Rules; Implic

  School: New York University

  Course: MATH 211.001

  ... Calculate the marginal revenue when q = 10. Solution: The marginal revenue, MR, is obtained by differentiating the total revenue function, R. We use the chain rule so MR = dR dq = 1 1 + 1000q2 · d dq (1000q2) = 1 1 + 1000q2 · 2000q. ...

• 1 Page

  • Assignment 4 Chain rule

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  Assignment 4 Chain rule

  School: University Of Waterloo

  Course: MATH 237

  MATH 237 ASSIGNMENT 4: Chain Rule Winter 2015 Submit your work at ... 1. Let w = x2y + xy3,x = 3t + 5,y = 2t2 - 10. Use the chain rule to calculate dw dt when t = -2. 2. Write the chain ...

• 3 Pages

  • MATH 204 Fall 2007 Assignment 3 Solutions

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  MATH 204 Fall 2007 Assignment 3 Solutions

  School: McGill University

  Course: MATH 204

  MATH 204 - SOLUTIONS 3 1. (a) The derivative can be obtained using the chain rule; the derivative of the term (yi − β0 − β1xi)2 with respect to β0 is 2 × (yi − β0 − β1xi) × (−1) = −2(yi − β0 − β1xi) ...

• 4 Pages

  • Homework 4

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  Homework 4

  School: University Of Toronto, Mississauga

  Course: MATH 21aY

  Math 21a: Multivariable calculus Homework 4: Chain Rule This homework is due Wednesday, 10/16 rsp Tuesday 10/15. 1 [Compare Stewart 11.5: 2 ] Use the chain rule to find the derivative dz/dt for z = cos(x + 7y) , ...

• 2 Pages

  • 237_S15_asst5

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  237_S15_asst5

  School: University Of Waterloo

  Course: MATH 237

  MATH 237 Spring 2015 Assignment 5 Topics: Chain rule, directional derivatives, gradient vector Due: Friday June 12th 1. The partial dierential equation 2u 2u 2u 2u = c2 + + t2 x2 y 2 z 2 () is the three dimensional wave equation. ...

• 2 Pages

  • Q_Differentiation and rates of change

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  Q_Differentiation and rates of change

  School: The Hong Kong University Of Science And Technology

  Course: MATH 1013

  ... on Dierentiation and Rates of Change Working with implicit dierentiation and logarithmic dierentiation - just another usage of the chain rule. ...

• 29 Pages

  • hw6-sol

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  hw6-sol

  School: Cornell University

  Course: MATH 1920

  14.6 The Chain Rule (LT Section 15.6) ... 4. According to the Chain Rule, ∂f/∂r is equal to (choose the correct answer): ...

• 5 Pages

  • Homework 2 answers

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  Homework 2 answers

  School: University Of Utah

  Course: MATH 1220

  ... Using Dx lnx = 1/x and the chain rule gives Dx ln(3x3 +2x) = 9x2+2 3x3+2x . Correct Answers: • (9*x**2+2)/(3x**3 + 2*x) ... Applying the definition of the derivative of the natural loga- rithm and using the chain rule shows the answer is 3 ...

• 4 Pages

  • 15.6%20Ex%2036%20-%2041

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  15.6%20Ex%2036%20-%2041

  School: University Of California, Los Angeles

  Course: MATH 32A

  ... Equalities (1) and (2) imply that: ∂u ∂t = −c ∂u ∂x or ∂u ∂t + c ∂u ∂x = 0 35. Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of θ (Figure 3). Suppose that Matthew runs wi...

• 5 Pages

  • HW 5

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  HW 5

  School: University Of Texas

  Course: M 427L

  ... 6. fxy = x 1 + x2y2 Explanation: Differentiating f partially with respect to x, using also the Chain Rule and d dx tan−1 x = 1 1 + x2 , ... keywords: partial differentiation, mixed par- tial derivative, Chain Rule, inverse tangent, 002 10.0 ...

• 1 Page

  • h5

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  h5

  School: University Of California, Irvine

  Course: MATH 2D

  ... 2. Using the chain rule, compute ∂z ∂t if z = cos(x + 4y) x = 5t4 y = 1 t 3. If z = f(x, y), x = r cos θ, and y = r sin θ, use the chain rule to prove that ∂2z ∂x2 + ∂2z ∂y2 = ∂2z ∂r2 + 1 r2 ∂2z ∂θ2 + 1 r ∂z ∂r ...

• 5 Pages

  • GW10(1)

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  GW10(1)

  School: University Of Illinois, Urbana Champaign

  Course: MATH 234

  ... The chain rule is a derivative law used to take derivatives of composite functions (functions which are plugged into other functions). ... Chain Rule Version II:Suppose you have a function that you write as a composite: y = f(u) u = g(x) ...

• 2 Pages

  • hw_10_sol

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  hw_10_sol

  School: University Of Utah

  Course: MATH 3220

  Solutions of Tenth Homework Solution of 9.3 Ex. 8: Define the function H(s, t) = (st, s + t), (s, t) ∈ R2. Then, we have G(s, t)=(F ◦ H)(s, t) for (s, t) ∈ R2. By the chain rule, we have dG(s, t ...

• 4 Pages

  • prob7sol

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  prob7sol

  School: San Diego State University

  Course: MATH 534A

  ... f (t)dt, so that F (x) = H (g (x)). By the chain rule and the Fundamental Theorem of Calculus, d dxF (x) = à dH (u) du ¯¯¯¯µdg (x) dx ¶ = (f (g (x))) dg (x) dx . ... By the chain rule and the Fundamental Theorem of Calculus. d dxZ �...

• 2 Pages

  • Hint2

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  Hint2

  School: National University Of Singapore

  Course: MATHEMATIC MA3110

  MA3110 Mathematical Analysis II Hints on Tutorial 2 H1. (i) Use the Binomial formula (x + h)n = n ∑ k=0 ( n k ) hk xn−k. H2. (i) Use the product rule and the chain rule. (ii) Use the definition of g (0) and the Squeeze Theorem. ...

• 2 Pages

  • Worksheet5(1)

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  Worksheet5(1)

  School: University Of Maryland, Baltimore County

  Course: MATH 151

  Math 151: Calculus I March 1, 2016 Section 3.4: Chain Rule 1. Find dy dx . (a) y = sin(5x) (b) y = (sin(x) + x4)5 (c) y = cos(8x) + / e3x + 4x (d) y = (2x + 5)18 (e) y = (x4−3)3 √ x2−1 (f) y = sin2 x5 + 4x (g) y = x / x2 + 1 ...

Chain Rule Lab Reports

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  • Nicholas Terrones Week 2 Lab Page 4 GRADED 1 - 23 - 16 DR

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  Nicholas Terrones Week 2 Lab Page 4 GRADED 1 - 23 - 16 DR

  School: DeVry University, Chicago

  Course: MATH 260

  Category 4: Chain Rule ... 6.) Describe, in your own words, how to find the derivative using the Chain Rule, then find the ...

• 2 Pages

  • MA103_W14_wk6solns

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  MA103_W14_wk6solns

  School: Wilfred Laurier University

  Course: MA 103

  MA103 Week 6 Report - Chain Rule; Implicit Differentiation; Logarithms Name: Student Number: Lab Winter 2014 ...

• 8 Pages

  • M137-week5

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  M137-week5

  School: University Of Waterloo

  Course: MATH 137

  ... 1. Chain Rule revisited Chain Rule. [f(g(x))] = f (g(x)) · g (x) Remark. In Leibniz notation, if y = f(u) with u = g(x), then Chain Rule says ...

• 1 Page

  • MTH-240-Lab12

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  MTH-240-Lab12

  School: Ryerson University

  Course: MTH MTH240

  Ryerson University Lab 12 - MTH 240 1. Problem 7 Section 14.5 Use the chain rule to nd z/s and z/t. z = x2 y 3 , x = s cot t, y = s sin t 2. Problem 21 Section 14.5 Use the chain rule to nd z/s, z/t and z/u when s = 4, t = 2, u = 1. z = x4 + x2 y ...

• 16 Pages

  • MATH277Lab5

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  MATH277Lab5

  School: University Of Calgary

  Course: MATH 275

• 3 Pages

  • lab H mth 241 differentiation practice, graph interpretation

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  lab H mth 241 differentiation practice, graph interpretation

  School: Oregon State University

  Course: MTH 241

Chain Rule Notes

• 4 Pages

  • exam2solutions

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  exam2solutions

  School: University Of Georgia

  Course: MATH 2250

  Math 2250 Exam #2 Solutions 1. Find the derivatives of the following functions. (a) f(x) = ln(tan−1 x) Answer: Using the Chain Rule, f (x) = 1 tan−1 x d dx (tan−1 x) Remembering that the derivative of tan−1 x is 1 1+x2 , the above becomes ...

• 2 Pages

  • lab3_f11

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  lab3_f11

  School: University Of Waterloo

  Course: MATH 116

  Math 116 - Lab 3 - Fall 2011. Rules for differentiation, chain rule, derivatives of trig, exponential, hyperbolic, inverse trig and inverse hyperbolic functions (Sections 3.3, 3.5-3.7 of L/G). You are to provide full solutions to the following pro...

• 1 Page

  • 265Lesson11Problems(3)

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  265Lesson11Problems(3)

  School: University Of North Dakota

  Course: MATH 265

  MATH 265: MULTIVARIABLE CALCULUS: LESSON 11 PROBLEMS Problems are worth 20 points each. (1) Let f(u, v) = u + v + uv2 and u = u(x, y) = ex + y, v = v(x, y) = xy. Use the Chain Rule to compute ∂f ∂x and ∂f ∂y . (2) Repeat problem 1, but thi...

• 12 Pages

  • Practice2S

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  Practice2S

  School: University Of Illinois, Urbana Champaign

  Course: MATH 231E

  Math 231E. Fall 2013. Midterm 2 Practice Solutions. Problem 1. Compute the derivatives of the following functions a. f(x) = cos(x2)esin(x) b. f(x) = arctan(x) c. f(x) = ln(ex(1 + x2 + x3)) Solution: a. We use the product and chain rules. We have d...

• 4 Pages

  • Math 10A Notes - The Chain Rule

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  Math 10A Notes - The Chain Rule

  School: University Of California, San Diego

  Course: MATH 10A

  ... The Chain Rule: Or, if and then =. Example: =. =. =. =. ... Example: [Product Rule]. [Chain Rule]. Example: [Quotient Rule]. Alternatively: ...

• 2 Pages

  • 3.4 Preclass Homework - Chain Rule-solutions

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  3.4 Preclass Homework - Chain Rule-solutions

  School: University Of Texas

  Course: M 408N

  schreiber (mcs3445) – 3.4 Preclass Homework - Chain Rule – maxwell – (55700) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find ...

• 8 Pages

  • Practice1S

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  Practice1S

  School: University Of Illinois, Urbana Champaign

  Course: MATH 231E

  ... x = sec(y). Differentiating both sides gives 1 = sec(y) tan(y) dy dx = sin(y) cos2(y) dy dx , so dy dx = cos2(y) sin(y) . Draw a triangle with near side of length x and far side of length 1, and if the interior angle is y, then sec(y) = x. Sin...

• 6 Pages

  • 15.2

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  15.2

  School: Drexel University

  Course: MATH 102

  Section 15.2 Substitution The indefinite integral formulas from section 15.1 are based on the derivative formulas. Now let's consider the chain rule. • Reversing the Chain Rule The indefinite integral of x e is C e dxe x x + = / . In order to...

• 3 Pages

  • Lab_2

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  Lab_2

  School: DeVry University, Ft. Washington

  Course: ACC Math 221

  ... Part 3. Milk Production. 1. Find the sample mean. 2270.54 is the sample mean. 2. Find the sample standard deviation. 653.1822 is the standard deviation. 3. Make a frequency distribution for the data. Distribution is started at right. Frequency...

• 3 Pages

  • Math 123 Finals Mass Tutorial

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  Math 123 Finals Mass Tutorial

  School: McGill University

  Course: BUSINESS 101

  ... y = -1/5x + 12/5 Same thing as: 4x+2y ≤ 20 x+5y ≤ 12 Solution Maximize P = 10x 1 + 8x 2 Subject to: y ≤ -2x + 10 y ≤ -1/5x + 12/5 x 1 , x 2 ≥ 0 Corner points: P(0,0) = 0 P(0,12/5) = 96/5 P(5,0) = 50 P(38/9, 14/9) = 164/3 (38/9, 14/...

• 2 Pages

  • 03 - Chain Rule with Logs Exponentials

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  03 - Chain Rule with Logs Exponentials

  School: Fairfield High School, Fairfield

  Course: CALCULUS 1

  Kuta Software - Infinite CalculusName_Differentiation - Logs and ExponentialsDate_ Period_Differentiate each function with respect to x.1) y = 44x42) y = 43) y = log 3 3 x 25) y = log 3 (3 x 5 + 5)7) y = (4 + 2)x39) y = 35 x 34) y = log 2 4.

• 2 Pages

  • 03 - Chain Rule with Trig

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  03 - Chain Rule with Trig

  School: Fairfield High School, Fairfield

  Course: CALCULUS 1

  Kuta Software - Infinite CalculusName_Differentiation - Trigonometric FunctionsDate_ Period_Differentiate each function with respect to x.1) f ( x) = sin 2 x 32) y = tan 5 x 33) y = sec 4 x 54) y = csc 5 x 55) y = (2 x 5 + 3)cos x 22 x 2 56) y.

• 4 Pages

  • 1_2_Chain%20Rule

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  1_2_Chain%20Rule

  School: University Of New South Wales

  Course: MATH 2019

  1.2 THE CHAIN RULE The Chain Rule for functions of more than one variable: If z = f(x, y) and x = x(t) and y = y(t) then ∂z ∂t = ∂z ∂x ∂x ∂t + ∂z ∂y ∂y ∂t If z = f(x, y) and x = x(u, v) and y = y(u, v) then ...

• 18 Pages

  • MATH283_L02

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  MATH283_L02

  School: University Of Wollongong, Australia

  Course: MATH 283

  Lecture 2: Chain Rule & Second Order Partial Derivatives ... introduce partial derivative of functions of n variables introduce chain rule for functions of several variables define higher order partial derivatives - second order partial deriva...

• 12 Pages

  • Math295-September28-Lecture

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  Math295-September28-Lecture

  School: Syracuse University

  Course: MAT 295

  2.5 - The Chain Rule September 28, 2012 Math 295-100 2.5 -The chain rule. 9/28/2012 1 / 11 The Chain Rule d dx (f (g(x)) = f (g(x)) · g (x) Or, if y = f (u) and u = g(x), dy dx = dy du · du dx ...

• 15 Pages

  • M119_LecNotes_017_SANS_Solutions_B3CAIA11_4158-

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  M119_LecNotes_017_SANS_Solutions_B3CAIA11_4158-

  School: Indiana University, Purdue University Indianapolis

  Course: MATH 119

  Math M119 1.7 – Page 1 of 15 SS 1 of 15 The Chain Rule OBJECTIVE • Find the composition of two functions. • Differentiate using the Extended Power Rule or the Chain Rule. 1.7 – Page 2 of 15 SS 2 of 15 ...

Chain Rule Test Prep

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  • MAT 267- Exam 2 Practice Questions with answers

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  MAT 267- Exam 2 Practice Questions with answers

  School: Arizona State University

  Course: MAT 267

  ... Test 2 Solutions 1) Use the chain rule to find ∂z ∂s if z = exy, x = 7s + 8t, y = st4. Applying the chain rule, we have ∂z ...

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  • Exam2Type1Sol

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  Exam2Type1Sol

  School: San Diego State University

  Course: MATH 252

  ... 1. We have d dx F (x, y (x)) = 0 for each x ∈ J. By the chain rule, 0 = d dx F (x, y (x)) = dF (x, y) dx + dF (x, y) dy dy dx Therefore, dy dx= − ...

• 19 Pages

  • Final Exam Study Guide on Calculus II

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  Final Exam Study Guide on Calculus II

  School: University Of Illinois, Chicago

  Course: MATH 181

  ... 1. Differentiate the function: F(x) = ∫ x2 √x et3 dt Solution: Using the Fundamental Theorem of Calculus Part II and the Chain Rule, the derivative of F(x) = ∫ h(x) g(x) f(t) dt is: F′(x) = d dx ∫ h(x) g(x) f(t) dt ...

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  • Chain Rule HW 2

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  Chain Rule HW 2

  School: Estrella Mountain Community College

  Course: MAT 220

  MAT 220 CHAIN RULE HOMEWORK 2: TRIGONOMETRIC DERIVATIVES Determine the derivative of each function. ...

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  • calc final cheat sheet

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  calc final cheat sheet

  School: Oklahoma State University

  Course: MATH 2103

  DERIVATIVE RULESd/dt (ekt) = kektd/dx (lnx) = 1/xd/dt (et) = etd/dx (ax) = (lna)axif y=clnx, then dy/dx = c/xTHE CHAIN RULE: d/dt (f(g(t) = f I(g(t) x gI(t)PRODUCT RULE: (fg) I = f I g + fg IQUOTIENT RULE: (f/g) = f I g fg I / g2PERIODIC : P ...

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  • Test 2 Review

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  Test 2 Review

  School: Louisiana State University

  Course: MATH 1550

  3.1-3.4. Know all the derivative rules – Basic rules, Quotient and product rule, Trig derivative rules, inverse trig rules, derivative of e x , derivative of ln x , and all chain rule variations. p181 #'s 3-30, 34,37. p189 #'s 3-24, 27-30...

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  • Practice_Midterm_2

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  Practice_Midterm_2

  School: Gettysburg College

  Course: MATH 211

  ... Section 14.5: The Chain Rule • Section 14.6: Directional Derivatives and the Gradient Vector ... 1. By the chain rule dz dt = df dt = ∂f ∂x dx dt + ∂f ∂y dy dt . Thus dz dt ∣ ∣ ∣ ∣t=1 = fx(g(1),h(1))g (1) + fy(g(1),h(1))h (1) ...

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  • quiz2solution

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  quiz2solution

  School: Temple University

  Course: CALC 1042

  Quiz 2 Math 1042.007, Calculus II, Spring 2016 Problem 1. (6 points) Let h(θ) = ∫ cos θ 0 ln(1 + x) dx, find d dθ h(θ). Solution: Let u(θ) = cosθ, then by the chain rule, we have d dθ h(θ) = d dθ ∫ u 0 ln(1 + x) dx = d du ∫ u 0 ln(1...

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  • Worksheet_011916_sol

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  Worksheet_011916_sol

  School: University Of Illinois, Urbana Champaign

  Course: MATH 241

  Tuesday, January 19 ∗ Solutions ∗ A review of some important calculus topics 1. Chain Rule: (a) Let h(t) = sin(cos(tant)). Find the derivative with respect to t. Solution. d dt (h(t)) = d dt (sin(cos(tant))) = cos(cos(tant))· d dt (cos(tant))...

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  • 121616949-math.133

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  121616949-math.133

  School: University Of California, Los Angeles

  Course: MATH 31A

  ... x to mean dx/dt goes back to Newton and is still used for this purpose, especially by physicists.) If y is written in terms of x, ie, y = f(x), then this is easy to do using the chain rule: ... Using the chain rule, dy/dt = 2x · dx/dt. ...

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  • 121616949-math.73

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  121616949-math.73

  School: University Of California, Los Angeles

  Course: MATH 31A

  3.5 The Chain Rule 59 Now we need to compute the derivative of x √ x2 +1. This is a product, so we use the ... x2 +1+ √ x2 + 1. Finally, we use the chain rule: d dx √ x2 +1= d dx (x2 + 1)1/2 = 1 2 (x2 + 1)−1/2(2x) = x √ x2 + 1 . ...

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  • MATH177Lab4

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  MATH177Lab4

  School: University Of Calgary

  Course: MATH 117

  ... Note : Problems marked with () are left for students to do at home. 1. Let z x4 2xy , where x 1 sin(2t) , and y tln(1 t). Use the Chain Rule to find dz dt at t 0. 2. Let W x2 2xyz , where x(t) et , y(t) tan(3t) 1 , and z(t) cos 1(t). Find dW d...

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  • Copy of Math252-Exam3-Spring--2014 (4)

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  Copy of Math252-Exam3-Spring--2014 (4)

  School: San Diego State University

  Course: MATH 252

  Name:_ 1. Use the Chain Rule to find z / t at the point ( s, t ) ( 3,2) . zex 3 y , x ln(s 2t ) , y st . ... 1. Use the Chain Rule to find at the point . , , . abcde. ...

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  • Chain Rule Practice 2

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  Chain Rule Practice 2

  School: Estrella Mountain Community College

  Course: MAT 220

  MAT 220 CHAIN RULE PRACTICE 2 Determine the derivative of each function. Positive exponents only in all final answers. ...

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  • Chain Rule HW 1

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  Chain Rule HW 1

  School: Estrella Mountain Community College

  Course: MAT 220

  MAT 220 CHAIN RULE PRACTICE 3 Determine the derivative of each function. Positive exponents only in all final answers. ...

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  • test2_sol

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  test2_sol

  School: University Of Utah

  Course: MATH 5040

  ... xy Solution: By the chain rule have FF = f (x + y) and = f (x + y). ... Solution: By the chain rule have ∂F ∂x = f/(x + y) and ∂F ∂y = f/(x + y) ...