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

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

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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University of Michigan - Ann Arbor

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All right. We want to find Dy dx for the function Y equals three signs four X to do so we're going to rely on derivative shortcuts that we picked up along the way in multi rather single variable calculus as opposed to using this traditional definition of the derivative. So these rules are on the left rule zero derivative of sign X. Cosign X. The derivative of cosine X. Negative Synnex. We also have Rules one through three on the right. The power rule, the product rule and the chain rule. In this particular problem, we're gonna have to apply rule zero as well as rule three. The chain will to solve So Y equals three signed four. X is always already written in the form that's easy to differentiate so we can perceive to take the derivative. So three signed four X gives derivative. Dy dx equals three. Coast four X times four. Multiplied by four is because of the chain rule before X. Inside the sign. Therefore we have final solution 12 co sign of four x.

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