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Numerade Educator

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Problem 12 Easy Difficulty

Find the derivative of the function.
$ g(\theta) = \cos^2 \theta $

Answer

$-2 \cos \theta \sin \theta$

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Video Transcript

Here's our function. G up data equals co sign square data. And remember, when you see co sign square data, what it means is that you take in co sign data and squared it. So this is a composite function. We have one function inside another, and so we're going to differentiate it using the chain rule. And so that means we need to find the derivative of the outside function and multiply it by the derivative of the inside function. So are derivative will call g prime of data, and the outside function is the squaring function. And it's derivative would be if we bring down the two and then we raised the inside to the one to the first because we subtract one to get the new power. Now we multiply by the derivative of the inside and the inside is co sign data and the derivative of co sign is negative sign. So we have negative sign data, so we have our derivative and now we're just going to simplify so we can bring the negative and the two together and we have negative to co sign data signed data