x^3*e^x
x^((3*e)^x)
3 x x *e
d / 3 x\ --\x *e / dx
Apply the product rule:
f(x)=x3f{\left(x \right)} = x^{3}f(x)=x3; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}dxdf(x):
Apply the power rule: x3x^{3}x3 goes to 3x23 x^{2}3x2
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: x3ex+3x2exx^{3} e^{x} + 3 x^{2} e^{x}x3ex+3x2ex
Now simplify:
The answer is:
3 x 2 x x *e + 3*x *e
/ 2 \ x x*\6 + x + 6*x/*e
/ 3 2 \ x \6 + x + 9*x + 18*x/*e