Suppose h =f\circ g . Find h'(0) given that f(0) = 4, f '(4) = -7,\;g(0) = 4 , and g '(0)...


Suppose {eq}h =f\circ g {/eq}. Find {eq}h'(0) {/eq} given that {eq}f(0) = 4, f '(4) = -7,\;g(0) = 4 {/eq}, and {eq}g '(0) = 1. {/eq}

Chain Rule:

We apply chain rule if we are asked to evaluate the derivative of a composite function.

Suppose we are given the composite function {eq}f(g(x)) {/eq}.

Applying the chain rule:

{eq}D_x(f(g(x)) = f'(g(x))g'(x) {/eq}

Answer and Explanation: 1

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First, we calculate {eq}h'(x) {/eq} by applying the chain rule:

{eq}\begin{align*} h(x)& =(f\circ g)(x) \\ h(x)& =f(g(x)) \\ h'(x)&...

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Learn more about this topic:

Using the Chain Rule to Differentiate Complex Functions


Chapter 8 / Lesson 6

Learn how to differentiate a function using the chain rule of differentiation. Find various chain rule derivative examples with various function types.

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