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Find the derivatives of the given functions.$$y=\sin (3 x+2)$$

$\frac{d y}{d x}=3 \cos (3 x+2)$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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what we want to find the derivative. Dy dx for Y equal signed three X plus two. At this point at our stage in single variable calculus, we should have picked up a series of shortcuts that'll make solving for this integral. But rather than derivative easier than using the typical definition of the derivative assets will apply those now. So the relevant rules are rules zero and left liberated of cyan X. Cossacks, Cossacks negative side. We also have the power rule. The product rule in the chain rule listed one through three on the right. Why is already of the form? That's most easy to differentiate. Three signed three exposed to. To solve. We're going to have to make use of rules zero and we'll three the chain rule. Thus we can proceed to our derivative as follows. So differentiating we have dy dx equals coast three X plus two times three. This is from the chain rule derivative of three experts. To thus, we have our final solution on the right three co sign three x plus two.

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