Question

usando as regras de derivação e da cadeia obtenha f'(x)

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Answer 1

$\displaystyle i)~~~~f(x)=e^{\sin x}\\\\ii)~~~\frac{df}{dx}=\frac{d}{dx}e^{\sin x}\\\\iii)~~u(x)=\sin(x)\\\\iv)~~~\frac{df}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\\\v)~~~~\frac{df}{dx}=\frac{d}{du}e^{u}\cdot \frac{d}{dx}\sin x\\\\vi)~~~\frac{df}{dx}=e^u\cos x=\boxed{\boxed{e^{\sin x}\cos x}}$
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