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Find the derivatives of the given functions.$$r=\tan (\sin 2 \pi \theta)$$

$\frac{d r}{d \theta}=2 \pi(\cos 2 \pi \theta) \sec ^{2}(\sin 2 \pi \theta)$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 2

Derivatives of the Other Trigonometric Functions

Derivatives

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we want to find do I. D. S. For the function? Why is equal to the tangent of sign of two PX. In this problem, we're going to use a derivative shortcuts. So we picked up for a single variable calculus in particular. We're going to make use of the trigonometry derivatives that we've recently learned. So I've listed all six trigonometry derivatives here in particular. We're obviously going to need to use sign derivative which is co sign X. And the tangent derivative which is you cant squared X. We'll also need to make use of the chain rule to solve so why is already written in the form that's most easily differentiable or the simplest form? Thus we can proceed straight to the derivative. So we're going to first apply the chain rule. We're gonna take the derivative of tangent with respect to what's inside and then we're gonna take the riverboats inside. So do I. D. X. Is you can't square designed by X. Times the derivative signed two PX which is co signed by excuse to pop, thus moving our constant outfront. Our solution is DY DX equals two pi coastline to pi X. Times you can't squared sine two PX.

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