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)#