Question

Найти производную y=xe^x (cosx+sinx)

Answer 1

$\displaystyle y=x*e^x(cosx+sinx)\\\\y`=(x*e^x*(cosx+sinx))`=\\\\e^x(cosx+sinx)+x*e^x(cosx+sinx)+x*e^x(-sinx+cosx)=\\\\=e^x(x(cosx+sinx-sinx+cosx)+cosx+sinx)=\\\\=e^x(x*2cosx+cosx+sinx)$

Answer 2

$y=xe^{x}*(cosx+sinx) \\ y'=e^x*cosx+e^x*sinx+2xe^x*cosx= \\ =e^x(cosx+sinx+2x*cosx)$