Chapter 3.2, Problem 46E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# If h(2) = 4 and h'(2) = –3, find d d x ( h ( x ) x ) | x = 2

To determine

To find: The value of ddx(h(x)x)|x=2.

Explanation

Given:

The values h(2)=4Â andÂ hâ€²(2)=âˆ’3.

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]âˆ’f1(x)ddx[f2(x)][f2x]2

(2) Power rule: ddx(xn)=nxnâˆ’1

Calculation:

Obtain the value of ddx(h(x)x)|x=2.

That is, compute ddx(h(2)2).

Substitute the h(x) for f1(x) and x for f2(x) in quotient rule (1),

ddx(h(x)x)=xddx(h(x))âˆ’h(

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