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Chapter 2: Q. 10 (page 209)

Suppose g, h, and j are differentiable functions with the values for the function and derivative given in the following table:

Use the table to calculate the values of the derivatives listed in Exercises 9鈥�16.

If f(x)=h(g(x)), findf'(3)

Short Answer

Expert verified

The value off'(3)=0

Step by step solution

01

Step 1. Given information

Function is: f(x)=h(g(x))

Given table:


02

Step 2. Find f'(3) using chain rule: 

Sincef(x)=h(g(x))

Hence, according to the chain rule of derivative:

f'(x)=h'(g(x))脳g'(x)f'(3)=h'(g(3))脳g'(3)

From the given table we can see that

g(3)=-3g'(3)=0

Substitute all these values in the above derivative:

f'(3)=h'(0)脳0=0

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