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Chapter 2: Q. 13 (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(j(x))), find f'(1).

Short Answer

Expert verified

The value off'(1)=4

Step by step solution

01

Step 1. Given information:  

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

Given table:


02

Step 2. Find f'(1) using chain rule:    

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

Hence, according to the chain rule of derivative:

f'(x)=h'(g(j(x)))脳g'(j(x))脳j'(x)f'(1)=h'(g(j(1)))脳g'(j(1))脳j'(1)

From the given table we can see that

j(1)=-2j'(1)=-1

Substitute all these values in the above derivative:

f'(1)=h'(g(-2))脳g'(-2)脳(-1)

From table,

g(-2)=1g'(-2)=2

So,f'(1)=h'(1)脳2脳(-1)=-2h'(1)=-2脳-2=4

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