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

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Answer 1 · 2018-03-26T11:29:40

$\frac{d y}{d x} = e^{x} (cos x + sin x)$ $dy/dx = e^x (cosx + sinx)$

$\frac{d y}{d x} = cos x \times e^{x} + e^{x} \times sin x$ $dy/dx = cosx xx e^x + e^x xx sinx$

$\frac{d y}{d x} = e^{x} (cos x + sin x)$ $dy/dx = e^x (cosx + sinx)$

Answer 2 · 2018-03-26T11:34:35

$e^{x} sin (x) + e^{x} cos (x)$ $e^xSin(x)+e^xCos(x)$

$f (x) = e^{x} sin (x) = e^{x} \times sin (x)$ $f(x)=e^xSin(x)=e^x times Sin(x)$

Using the product rule

$f'(x)=uv'+vu'$

$u=Sin(x)$
$u'=Cos(x)$

$v=e^x$
$v'=e^x$

Hence:
$f'(x)=e^xSin(x)+e^xCos(x)$

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