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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Suppose f(π/3) = 4 and f'(π/3) = –2, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find

(a) g'(π/3)

(b) h'(π/3)

(a)

To determine

To find: The differentiation of g(x)=f(x)sinx.

Explanation

Given:

The function is g(x)=f(x)sinx and f(π3)=4, f(π3)=2

Formula used:

Product Rule:

Product rule for two functions f1(x) and f2(x) is given as follows.

ddx[g1(x)g2(x)]=g1(x)ddx[g2(x)]+g2(x)ddx[g1(x)] (1)

Calculation:

Apply Product Rule as shown in equation (1).

In equation (1), substitute f(x) for g1(x) and sinx for g2(x).

ddx(f(x)sinx)=f(x)ddx(sinx)+sinxddx(f(x))=f(x)(cosx)+sinx(f′</

(b)

To determine

To find: The differentiation of h(x)=cosxf(x).

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