   Chapter 2.4, Problem 29E

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# If H ( θ ) = θ sin θ , find H ′ ( θ ) and H ″ ( θ ) .

To determine

To find: H'θ and H" (θ)

Explanation

1) Formula:

i. Product rule:

ddxfx*gx=fxddxgx+gxddxfx

ii. Sum rule:

ddxfx+gx=ddxfx+ddx(gx)

iii. Derivative of sine:

ddxsinx=cosx

iv. Derivative of cosine:

ddxcosx=-sinx

2) Given:

Hθ=θsinθ

3) Calculations:

Hθ=θsinθ

Differentiate Hθ with respect to θ,

H'θ=ddθ(θsinθ)

By using product rule,

H'θ=θddθsinθ+sinθddθ(θ)

By using formula,

H'θ=θcosθ+sinθ(1)

H'θ=θcos

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