   Chapter 2.4, Problem 15E

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# Differentiate. f ( θ ) = θ cos θ sin θ

To determine

To differentiate: the given function using differentiation rules.

Explanation

1) Concept:

f(θ) is product of three functions that is θ,sinθ, and  (cosθ). So to find the derivative of   f(θ) , use product rule.First use product rule for  (θcosθ) and   (sinθ). Again for derivative of ( θcosθ) use product rule, and then use standard differentiation rule.

2) Formula:

i. Product rule:

ddxfx*gx=fxddxgx*g(x)ddxf(x)

ii. Derivative of sine:

ddxsinx=cosx

iii. Derivative of cosine:

ddxcosx=-sinx

3) Given:

f(θ)=θsinθcosθ

4) Calculations:

Using product rule:

ddθ(fθ)=sinθddθθcosθ+θcosθddθ(sinθ)

Compute the derivatives using product, sine and cosine rules

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