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Find the derivatives of the given functions.$$y=4 \cos ^{2} \sqrt{x}$$

$\frac{d y}{d x}=12 x \cos 3 x+4 \sin 3 x$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Oh we want to find DY DX for the function Y is equal to four coastline square square ducks in this problem. We're gonna rely on derivative shortcuts, specifically those related. We're gonna get through this to solve. So we have the most relevant rules. Let's sit here is 0 to 30 is DDX in Mexico's Cossacks and DDX Cossacks as negative Sine X. We also have Rules one through three. The power rule product ruling chain rule respectively. In this particular problem we're going to have to rely on rule 01 and three to solve. So let's first put this in a form that's easier to use rule 013 This is why equals four. Co sign route X squared or Y equals four. Co sign extra one half squared. Thus we have D. I. D. X equals four times to co sign road X times 100 of us inside to get signed checks. The change will get get to apply to the inside of Sine X which gives one half X negative one half. Because we have final solution do I. D. X equals negative four over Route X. Co sign next signed X.

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