Question

If $y=e^x\sin x$, then find $\frac{dy}{dx}$

• A. $e^x(\sin x+\cos x)$
• B. $e^x(\sin x-\cos x)$
• C. $e^x\sin x$
• D. None of these

Answer 1

The correct option is A $e^x(\sin x+\cos x)$

Given that
$y=e^x.\sin x$
On differentiating, we get
$\frac{dy}{dx}=\sin x\frac{d}{dx}{e}^x+e^x\frac{d}{dx}\sin x$
$\frac{dy}{dx}=\sin x{e}^x+e^x\cos x$
$\therefore \frac{dy}{dx}=e^x(\sin x+\cos x)$