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Find the derivatives of the given functions.$$V=\left(4-\csc ^{2} 3 r\right)^{3}$$

$\frac{d V}{d r}=18 \csc ^{2} 3 r \cot 3 r\left(4-\csc ^{2} 3 r\right)^{2}$

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 the derivative. Dy dx for the function. Why equals four minus coast. You can't square of three are cubes. So to solve, we're going to proceed to define the relevant shortcuts that we need to solve its derivative specifically, we're going to rely on trigonometry derivatives we've recently learned. So the relative derivatives are listed here. Of the six trigger derivatives that I've listed. We really only need to rely on DDX coast. You can't X equals negative post. You can't tangent X. We also are going to use the chain rule to solve so we have Y equals four minus cost. You can't square through. Our cube is already in its most easy different to perform, which means we can proceed to the derivative. Thus we have dy Dx equals by the chain rule three times four minus coast. You can't square three R squared times what's inside which is negative. Two coast, you can't three are times negative coast. You can't three Arco tangent three times three. Which your final solution DY DX equals 18 times four minus coast. You can't square through r squared times cause you can't square three arc tangent three are.

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