x x*E
x*E^x
Apply the product rule:
f(x)=xf{\left(x \right)} = xf(x)=x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: xxx goes to 111
g(x)=exg{\left(x \right)} = e^{x}g(x)=ex; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}dxdg(x):
The derivative of exe^{x}ex is itself.
The result is: ex+xexe^{x} + x e^{x}ex+xex
Now simplify:
The answer is:
x x E + x*e
x (2 + x)*e
x (3 + x)*e