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Find the derivatives of the given functions.$$y=3 \cot 6 x$$

$\frac{d y}{d \theta}=-18 \csc ^{2} 6 x$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 2

Derivatives of the Other Trigonometric Functions

Derivatives

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mhm. We want to find the derivative. Why with respect to X. Dy dx for the function Y. Equals co Tandy xxx to do so. We're gonna rely on derivatives shortcuts we picked up throughout our journey and single variable count. So most relevantly we're gonna make a note of the trigger metric derivatives. These are D. D. X in X equal co sex DDX co sex negative sine X. D. X. 10 X equals decant square DDX co tangent X. Equals negative Costa can't squared and so on. We also make note of the chain rule product rule and so on. Other derivative shortcuts we've learned particularly for this problem. We need the derivative of tangent combined with the chain rule so we can rewrite as Y equals recruit and sex. That is our function is already the most differential form for the most easily defensible form. So dy dx is three times negative coast. Can't square six X. Is the tip of koh tangent. We multiply by six by the chain rule on six X. And give us a final solution. Dy dx equals negative 18 times coast. You can't squared six X.

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