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# Compute the Derivative of a Composed Function

APCALC-5TFPZE

Let $g'(x)=\cos x$ and $f(x)=\sin(x^2)$. Which of the following is equivalent to $\cfrac{d}{dx}(f(g(x))$?

A

$2\cos x \cdot g(x) \cdot \cos(g^2(x))$

B

$-\sin 2x \cdot \cos (\cos^2 x)$

C

$2x\cos(x^2) \cdot g(x) \cdot \cos(x)$

D

$\sin(x^2) \cos x+2x\cos(x^2)g(x)$