7 x x *E
x^7*E^x
Apply the product rule:
f(x)=x7f{\left(x \right)} = x^{7}f(x)=x7; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x7x^{7}x7 goes to 7x67 x^{6}7x6
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: x7ex+7x6exx^{7} e^{x} + 7 x^{6} e^{x}x7ex+7x6ex
Now simplify:
The answer is:
7 x 6 x x *e + 7*x *e
5 / 2 \ x x *\42 + x + 14*x/*e
4 / 3 2 \ x x *\210 + x + 21*x + 126*x/*e