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

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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)).`