`f(x) = ln(sin(x)^2)` Differentiate the function.

Textbook Question

Chapter 3, 3.6 - Problem 4 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to differentiate the function with respect to x, using the chain rule, such that:

`f'(x) = (ln(sin(x^2)))'`

`f'(x) = (ln'(sin(x^2)))*(sin'(x^2))*(x^2)'`

`f'(x) = (1/(sin x^2))*(cos(x^2))*(2x)`

`f'(x) = (2x*cos(x^2))/(sin x^2)`

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Hence, evaluating the derivative of the given function, yields `f'(x) = (2x*cos(x^2))/(sin x^2).` ` `

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