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Find the derivative of the following functions.$$y=w^{2} \sin w+2 w \cos w-2 \sin w$$

$w^{2}$ cos $w$

Calculus 1 / AB

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

Differentiation

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So what? This problem were asked to find the derivative of this function outlined here in black. And because we have various functions being multiplied together, we have to use the product full so we'll start this by breaking down each term. So what? This first term we can define A as W squared and a prime therefore will be to W. And we consent e as sign of W and be prime as co sign w. So for this first term, we can then outline the product rule as to W times sign of W plus W Squared Times Co sign of W mm we can rewrite that, then is to w sign of W plus W squared Co sign W. And that's our first term. A second term, which will put in green can I meet outlined as a Equalling um, to W and e prime. Therefore equaling two and be equaling who sign of W and be prime would then be negative sign W. So for this second term, we would have the product full as to Times Co sign of W plus two w times negative sign of W. And again, we can simple finalize to co signed of you minus two w Sign of W in this third term, which will then putting Blue will have a you go into and then a prime would be zero and be equaling sign of W and be prime equal in co sign of W. So for this we'll have the product rule as zero times Sign W, which cancels out 20 was to Times Co sign of W. So now we have the individual product rules of each so we can combine all the terms together sits Huw sign of W plus W Squared Co sign of W plus to co sign of W minus two w sign of W minus two co sign W In this negative here comes from the original equation, and what you'll notice is that we have the same terms grouped together that just so happened to cancel out. So our final answer, therefore is W squared co sign of W

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