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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

If g(θ) = θ sin θ, find g″(π/6).

To determine

To find: The value of g(π6).

Explanation

Given:

The function g(θ)=θsinθ.

Derivative Rule:

Quotient Rule: ddx[fg]=fddx[g]+gddx[f]

Calculation:

The first derivative of g(θ) is g(θ), which is obtained as follows,

g(θ)=ddθ(g(θ)) =ddθ(θsinθ)=θddθ(sinθ)+(sinθ)ddθ(θ)   (by product rule)=θcosθ+sinθ          (ddθ(θ)=1)

Thus, the first derivative of the function g(θ)=θsinθ is g(θ)=θcosθ+sinθ.

The second derivative of g(θ) is g(θ), which is obtained as follows.

g(θ)=ddθ(g(θ)) =ddθ(θcosθ+sinθ) =ddθ(θcosθ)+ddθ

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