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AP® Calculus AB-BC

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Chain Rule: Cubed Root of Cosecant

APCALC-L8ENSW

What is the derivative of $y=(\csc { \theta } )^{ \frac{1}{3} }$ with respect to ‘$\theta $’?

A

$\cfrac{dy}{d\theta}=-\cfrac{{ \cot { ( \theta ) } \csc ^{ \frac{1}{3} }{ ( \theta ) } } }{3}$

B

$\cfrac{dy}{d\theta}=-\cfrac{{ \cot { ( \theta ) } \csc ^{ \frac{1}{3}}{ ( \theta ) } } }{6}$

C

$\cfrac{dy}{d\theta}=-\cfrac{{ \cot { ( \theta ) } \csc ^{ \frac{4}{3} }{ ( \theta ) } } }{3}$

D

$\cfrac{dy}{d\theta}=3 \tan { ( \theta ) } \sec ^{ \frac{2}{3} }{ ( \theta ) }$

E

$\cfrac{dy}{d\theta}=-6\sec { ( \theta ) } \csc ^{ \frac{5}{3} }{ ( \theta ) }$