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Find the derivatives of the given functions.$$y=4 x \sin 3 x$$

$\frac{d v}{d t}=18 \pi t^{2} \cos 3 \pi t+12 t \sin 3 \pi t$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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All right. We want to find Dy Dx for the function. Y equals four X. Signed three X. So we're going to rely on derivative shortcuts. We picked up a single variable cut this all, especially those relating to training metric functions. So the most relevant rules are listed here. Rule zero G D X in Mexico's Cossacks. Tv expose expos negative syntax rules one through three are the powerful product rule and general, respectively. We're going to rely on all four of these rules to solve this particular derivative. So first Y equals four X and three X is already in the most easily form to differentiate. So we proceed straight to the derivative so we have derivative as follows. Dy dx is equal to four signed three X plus four X. Coast three X times three The terms and left and right are separated because of the product rule on the left. We apply the power rule for four X on the right. We apply we'll zero in the chain rule to turn sign three X in the coast. Three extends three. Thus be a final solution. DY DX is equal to four signed three X plus 12 X times the co sign of three X.

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