What is the derivative of this function  y=sin x(e^x)?

Mar 26, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{x} \left(\cos x + \sin x\right)$

Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos x \times {e}^{x} + {e}^{x} \times \sin x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{x} \left(\cos x + \sin x\right)$

Mar 26, 2018

${e}^{x} S \in \left(x\right) + {e}^{x} C o s \left(x\right)$

Explanation:

$f \left(x\right) = {e}^{x} S \in \left(x\right) = {e}^{x} \times S \in \left(x\right)$

Using the product rule

$f ' \left(x\right) = u v ' + v u '$

$u = S \in \left(x\right)$
$u ' = C o s \left(x\right)$

$v = {e}^{x}$
$v ' = {e}^{x}$

Hence:
$f ' \left(x\right) = {e}^{x} S \in \left(x\right) + {e}^{x} C o s \left(x\right)$