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

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Answer 1 · 2018-03-26T11:29:40

$dy/dx = e^x (cosx + sinx)$

$dy/dx = cosx xx e^x + e^x xx sinx$

$dy/dx = e^x (cosx + sinx)$

Answer 2 · 2018-03-26T11:34:35

$e^xSin(x)+e^xCos(x)$

$f(x)=e^xSin(x)=e^x times Sin(x)$

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=sin x(e^x)?