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Numerade Educator

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Problem 37 Medium Difficulty

Find the derivative of the function.
$ y = \cot^2 (\sin \theta) $

Answer

$=-2 \cos \theta \cot (\sin \theta) \csc ^{2}(\sin \theta)$

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Video Transcript

we're going to use the chain rule to find the derivative of this function. But first I'm going to rewrite the function. Remember, when you see co tangent squared, what it means is take the whole thing and square it so the squared is really the outermost function. So we have three layers here. The outermost function is the squaring function than the inner layer is a co tangent function and then the very most inside layer is the sine function. So let's start our derivative by taking the derivative of the outside function. So we bring down the two and we raise co tangent to the first. Now we move on to the middle layer, which is co tangent, and it's derivative is negative. Cosi can't squared, so have negative. Cosi can't squared of science data. Now we moved to the innermost layer the sign beta layer and we take its derivative with which is co sign data and to simplify. The only thing we can do is multiply the two and the negative together. So we have negative to times co tangent of science. Aita Times Coast. He can't squared of science data Times co sign data