   Chapter 2.R, Problem 64E

Chapter
Section
Textbook Problem

# 61–68 Find f ' in terms of g ' . f ( x ) = x a g ( x b )

To determine

To find:

f' in terms of g'

Explanation

Differentiate by using differentiation rules

1) Formula:

(i) Product rule:

ddxfx*gx=fxddxgx+gxddx(fx)

(ii) Chain rule:

ddx(fgx=f'gx*g'(x)

(iii) Power rule:

ddxxn=nxn-1

2) Given:

fx=xag(xb)

3) Calculation:

Consider the function, fx=xag(xb)

Differentiate the function with respect to x,

f'x=ddx(xagxb)

By using product rule,

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