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Find the derivatives of the given functions.$$y=2 \ln \tan 2 x$$

$\frac{d u}{d x}=\frac{4 \sec ^{2} 2 x}{\tan 2 x}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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mhm. We want to find the derivative dy dx for the function. Why is equal to two natural algorithm of tangent of two X. This question is testing our knowledge of differentiation shortcuts, particularly those for transcendental functions and even more specifically for logarithmic functions as such as defined the relevant rules for director of taking on the left. Our rules zero DDX log you into the Excel interview on the right. We have the power rule, product rule and chain will respectively. And this problem leading to use multiple zero and three the chain rule to solve so Y equals to Ellen tangent of two. X is already in its most easily defensible form and that's probably going to use dD Exelon. U equals one over you. D you D X for U equals 10 2 X. So we proceed to solve the U i d x is two times one over you won over 10 2 x times du dx. Which is he can't square two X times to buy the chain rule. Simplifying this expression gives us dY dx is equal to four times a C. Can't squared of two X, divided by the tangent of two X.

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