   Chapter 2.R, Problem 69E

Chapter
Section
Textbook Problem

# 69–71 Find h ' in terms of f ' .and g ' . h ( x ) = f ( x ) g ( x ) f ( x ) + g ( x )

To determine

To find:

h' in terms of f' and g'

Explanation

Differentiate by using differentiation rules

1) Formula:

(i) Product rule:

ddx[fx.g(x)]=f(x)ddxgx+g(x)ddxf(x)

(ii) Quotient rule:

ddxf(x)g(x)=g(x).ddxf(x)-f(x).ddxg(x)g(x)2

(iii) Sum rule:

ddxfx+gx=ddxfx+ddxgx=f'x+g'(x)

2) Given:

hx=fxg(x)fx+g(x)

3) Calculation:

h'(x)=ddxfxg(x)fx+g(x)

By using quotient rule,

ddxfxg(x)fx+g(x)=fx+gx.ddxfxgx-fxgx.ddx[fx+gx]fx+gx2

By using product and sum rule,

ddxfxg(x)fx+g(x)=fx+gx

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