Unit Three Notes Derivatives--Determining Change

Unit Three Notes Derivatives--Determining Change - Unit...

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Unit Three Notes—Determining Change 3.1 Drawing Rate of Change Graphs Ex 1: Given f(x) = x 2 – 2x + 2, draw f(x) and draw a rough estimate of ( 29 x f . Ex 2: Given f(x) = x 3 – 7x + 6, draw f(x), ( 29 x f , and ( 29 x f . Ex 3: Given ( 29 x f , draw a rough estimate of f(x) and ( 29 x f
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3.2/3.3 Simple Rate of Change Formulas of Polynomials, Power, Exponential, Logarithmic Functions Function: Derivative Formula: f(x) = constant f(x) = x n f(x) = mx + b f(x) = c●g(x) f(x) = g(x) ± h(x) f(x) = b x f(x) = e x f(x) = x b log f(x) = ln(x) Derivations of some of the formulas above using the formal definition:
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Ex 1: Find the derivatives of the following functions using the simple formulas. A) f(x) = x 5 B) f(x) = 8 C) f(x) = e D) f(x) = e x E) f(x) = 5 x F) f(x) = ln(x) G) f(x) = ( 29 x 5 log H) f(x) = -2x + 5 I) f(x) = 3x 7 J) f(x) = 4x 3 – 7x 2 + 15x – 10 K) f(x) = 2 x – ln(x) L) f(x) = ( 29 x e x x x - + - 5 log 2 4
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Brief Calculus Notes 3.4—Chain Rule T The Chain Rule If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f(g(x)) is a differentiable function of x and . . . dx du du dy dx dy = or ( 29 ( 29 [ ] ( 29 ( 29 ( 29 x g x g f x g f dx d = T The General Power Rule u is a function of x If y = [u(x)] n ( 29 ( 29
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This note was uploaded on 02/28/2012 for the course MAT MAT 212 taught by Professor Michaeldereck during the Spring '12 term at Mesa CC.

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Unit Three Notes Derivatives--Determining Change - Unit...

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