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Numerade Educator

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Problem 11 Easy Difficulty

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

Answer

$=-2 \theta \sin \left(\theta^{2}\right)$

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Video Transcript

here's our function, and it's a composite function because it has one function inside the other. And so we're going to find the derivative using the chain rule and so f prime of data. The derivative would be the derivative of the outside function times, the derivative of the inside function, and the outside function is co sign, and it's derivative is negative sign. So we have negative sign of data squared. Whatever was in there still in there times the derivative of the inside and the inside is they two squared, so it's derivative would be to fade up. Okay, so we have our derivative and now we just want to simplify it so we could multiply the tooth data and the negative one. And we have negative two theta sign of state a squared