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Find the derivatives of the given functions.$$z=0.2 \cos (4 \sin 3 \phi)$$

$\frac{d z}{d \phi}=-2.4 \sin (4 \sin 3 \phi) \cos 3 \phi$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Why we want to find dy dx the function Y equals point to co sign a four signed three X. To do so we're going to rely on derivative shortcuts. We picked up through a single variable kelp specifically rely on rules zero through three Here. Rules here on the left is D. V. X. And X. Disco sucks T. V. Exco sexy with negative side X. And Rules one through three. The power rule product rule in general, respectively. For this particular problem we rely primarily on rule zero on Rules three to solve so why equals point to co sign for sign three X. Is already in the most easily differential before. Therefore we don't have to be writing further. Next we differentiate so from rule zero we have do I. D. X equals negative two or rather negative 20.2 Sine for sine three X. By the chain rule. We multiply like four. Co sign three X times three. Thus we have solution. Do I. D. X equals negative 2.4. Co sign three X. Sign of four signed three X.

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