Differentiate y=e^(x)*sin(x) with respect to x

y=e^(x)*sin(x)   

Use the product rule:   y'=uv'+vu'    y=u*v          

Differentiate: u=e^(x)   u'=e^(x)    v=sin(x)  v'=cos(x)

Sub into the product rule: y'=e^(x)*cos(x)+e^(x)*sin(x)

Take out a factor of e^(x): y'=e^(x)*(cos(x)+sin(x))