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AP® Calculus AB-BC

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A Function with a Trigonometric Exponent

APCALC-4T418L

Let $f(x)$ be the function defined by: $f(x)={ x }^{ \sin { ( x ) } },x>0$

Find the derivative of $f$ evaluated at $x=\cfrac{\pi}{2}$.

A

$1$

B

The derivative does not exist at $\cfrac{\pi}{2}$.

C

$\cfrac{\pi}{2}$

D

$0$