`f(theta) = (1/4)(sin(2theta))^2` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 57 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the derivative of the function, hence you need to use the chain rule, differentiating first the power, then the sine function and then the argument, such that:

`f'(theta) = (1/4)((sin(2theta))^2)'*(sin 2 theta)'*(2 theta) `

`f'(theta) = (1/4)(2*sin(2theta))*(cos 2 theta)*2`

Simplifying by 4 yields:

`f'(theta) = (sin(2theta))*(cos( 2 theta))`

Hence, evaluating the derivative of the function, yields `f'(theta) = (sin(2theta))*(cos( 2 theta)).`

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