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Chapter 2: Q. 15 (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)=hg(x)jx, findf'(0)

Short Answer

Expert verified

The value off'(0)=-12

Step by step solution

01

Step 1. Given information:   

Function is: f(x)=hg(x)j(x)

Given table:

02

Step 2. Find f'(0) using chain rule:  

Sincef(x)=hg(x)j(x)

Hence, according to the chain rule of derivative:

f'(x)=h'g(x)jx脳ddxg(x)j(x)

Apply product rule:

f'(x)=h'g(x)j(x)脳g(x)j'(x)+j(x)g'(x)f'(0)=h'(g(0)j(0))脳g(0)j'(0)+j(0)g'(0)

From the given table we can see that

g(0)=2g'(0)=-2j(0)=0j'(0)=-2

Substitute all these values in the above derivative:

f'(0)=h'(2脳0)脳2(-2)+0(-2)=h'(0)-4+0=-4脳h'(0)

In table h'(0)=3

So,f'(0)=-4脳3=-12

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Most popular questions from this chapter

Use (a) the h鈫�0definition of the derivative and then

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