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Find the derivatives of the given functions.$$v=6 t^{2} \sin 3 \pi t$$

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

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Yeah, we want to find Dy Dx for the function Y equals six X squared sine three PX to do so we rely on the road in shortcuts we picked up throughout Singletary book up especially those related to trigger an electric derivatives. So the most relevant rules to solve this problem are now listed here have zero through three. These are rules zero DDX in Mexico's coast, 60 D expose. Xnegative syntax and rules 123 The power roll products ruling chain were respectively, will rely primarily on real 01 and three to solve. We also have to use the product rule. So all four rules here will be used. Why equal six X squared sine three PX is already the most easily differential reform. So you can see through the derivative. This gives do I D X equals 12 X sign of three pi X plus six X squared plus in three PX three pi we use the product rule to separate into the some separated by this plus sign on the left. We have the power rule for six X squared on the right, the chain rule and rule zero for 73 PX. From this, we obtain our final solution for DY dx as 12 X. Sign three PX plus 18 Y X squared. Co sign three PX.

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