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Numerade Educator

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Problem 4 Easy Difficulty

Differentiate the function.

$ f(x) = \ln (\sin^2 x) $

Answer

2 $\cot x$

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Video Transcript

So for this problem, we want to be able to take the derivative of functions log rhythmic functions in particular. So first thing we want to recall is that the natural log of A to the B is the same as b times, the natural log of a So, since we have the natural log of sine X squared, we can rewrite this as the natural a two times the natural log of Synnex. Then we'll take the derivative of this. So we'll have to over the sign of X times the co sign of X, because that is taking the chain rule, we take the derivative of this, which is co sign of X s. So now what we end up seeing as a result is that co sign of X over sign of X is just the co tangent of X. So our final answer is the F prime of X is equal to two times the co tangent of X and the way that we can show us to be The case is if we look, we see that this purple graph right here is our derivative, and it's the same as F prime of X. So that right there shows us that our graph is correct because we end up getting the same values as a result.