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Find the derivatives of the given functions.$$r=0.4 e^{2 \theta} \ln \cos \theta$$

$\frac{d r}{d \theta}=-0.4 e^{2 \theta} \tan \theta+0.8 e^{2 \theta} \ln \cos \theta$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

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All right. We want to find dy dx four. Y equals 0.4. Either the two X. Natural algorithm of coastline of X. So we're going to rely on derivative shortcuts to solve in particular. Well, zero through three listed here on the left, zero is G D X P T U equals B U l n b d s G exceeded the EU is either the U d X rules one through three Other power world product rule and change respectively. Y equals point for each of the two. XL and Cossacks has already written it's most easily differential form. Thus we can proceed to solve, we see that we're gonna have to use the product wolf to separate out either the two X and Ellen Cossacks derivatives. So we have dy dx equals point for each of the two X times two Ln Cossacks is using real zero on each of the two X plus point for each of the two X times negative seven X. Over Cossacks. This is using the fact that the derivative of Ln. You is do you over you where coastline has a lot of negative sign that we can simplify this as dy dx equals each of the two X times 20.8 Ln cossacks minus 0.4 tangent of X. Remember that Synnex over Cossacks equals tantric.

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