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AP® Calculus AB-BC

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Moderate

Product Rule with Polynomial and Tangent

APCALC-BIXS4O

What is the derivative of $y=-2{ x }^{ 3 }\tan \left( {\cfrac{x}{2}} \right) $ with respect to $x$?

A

$\cfrac{dy}{dx}=-4\left[2x^3\cot^2\cfrac{x}{2} +3{ x }^{ 2 }\tan \left( {\cfrac{x}{2}} \right) \right]$

B

$\cfrac{dy}{dx}=-6x^2\tan\left( {\cfrac{x}{2}} \right) -x^3\sec^2 \left( {\cfrac{x}{2}} \right)$

C

$\cfrac{dy}{dx}=-2x^3\sec^2\left( {\cfrac{x}{2}} \right) +3x^2\tan \left( {\cfrac{x}{2}} \right)$

D

$\cfrac{dy}{dx}=-x^3\cot\left( {\cfrac{x}{2}} \right)\csc\left( {\cfrac{x}{2}} \right) +3x^2\sec^2 \left( {\cfrac{x}{2}} \right)$