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Chapter 2: Q. 25 (page 198)

Suppose g(x), h(x), and j(x) are differentiable functions with the values of the function and its derivative given in the following table:


x g(x) h(x) j(x) g'(x) h'(x) f'(x)
-1 3 0 1 -1 -2 -2
0 2 3 0 -2 3 -2
1 0 -1 -2 -2 -2 -1
2 -2 -2 -3 -1 0 2
3 -3 0 1 0 1 2

f(x)=g(x)(h(x)+j(x)) find f'(2)

Short Answer

Expert verified

The value isf'(2)=1

Step by step solution

01

Given information

We are given a table

x g(x) h(x) j(x) g'(x) h'(x) f'(x)
-1 3 0 1 -1 -2 -2
0 2 3 0 -2 3 -2
1 0 -1 -2 -2 -2 -1
2 -2 -2 -3 -1 0 2
3 -3 0 1 0 1 2
02

Calculate

f'(x)=g'(x)[h(x)+j(x)]+g(x)[h'(x)+j(x)]f'(2)=g'(2)[h(2)+j(2)]+g(2)[h'(2)+j(2)]f'(2)=-1[-5]+(-2)[0+2]f'(2)=5-4f'(2)=1

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