Implicit Differentiation
Until this point all the functions we have found the derivative of have been in
EXPLICIT form, that is y=_, we will now find the derivative of functions that
are in IMPLICIT form, y and x
1.1 Introduction to Calculus
PreCalculus
Calculus
Today we are going to explore both of these situations.
Consider the following graph of y = x 2 + 1 .
Suppose we want to find the sl
Kuta Software ~ Infinite Calculus Name
Differentiation Product Rule Date Period
Differentiate each function with respect to x.
1) y = x3(3x4 2) 2) f(x) = x2(-3x2 2)
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{.512 x ~§ 3.3; «3.
Product and Quotient Rules
The Product Rule
We use the product rule to find the derivative of two functions that are being
multiplied together so that we can find the derivative faster than having to multiply
the
Calculus Name
Power' Rule Workshee1L Block Dare
Find The derivarive of each function.
1-):X8 2 y=§/;/ 3 Y=X5_ 4. V(F)=7rr'3 5.)(7)=67"9 0K
~7 I :c, ~76
7 t 3 - f D. U ,
31:5! \l A :X: {1% 3 v/(r):§77;r V( n 'W
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3.5 3.7 Fizz
Find the limit at infinity.
2x 1
x 3 x + 2
1. lim
2 x10 1
x 10 x 11 3
2. lim
3. lim
x
2x + 1
x2 x
6. Find the length and width of a rectangle that has a perimeter of 80 and a maximum
area.
7. A rectangular page contains 24 square inche
INTRO TO CALCULUS
REVIEW FINAL EXAM
NAME:
DATE:
A. Equations of Lines (Review Chapter)
y = mx + b (Slope-Intercept Form)
Ax + By = C (Standard Form)
y y1 = m(x x1) (Point-Slope Form)
Problems:
1.
Find the equation of a line passing through point (5, -2) w