AP Calculus ABhardmcq1 pt

If f(x)=esin(3x)f(x)=e^{\sin(3x)}, then f(x)=f'(x)=

A.esin(3x)e^{\sin(3x)}
B.3ecos(3x)3e^{\cos(3x)}
C.cos(3x)esin(3x)\cos(3x)e^{\sin(3x)}
D.3cos(3x)esin(3x)3\cos(3x)e^{\sin(3x)}

Explanation

Core Concept

The derivative of eue^u is euue^u u' with u=sin(3x)u=\sin(3x). Since u=3cos(3x)u'=3\cos(3x), the result is 3cos(3x)esin(3x)3\cos(3x)e^{\sin(3x)}.

Correct Answer

D3cos(3x)esin(3x)3\cos(3x)e^{\sin(3x)}

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