x^2*e^(x^2)
/ 2\ 2 \x / x *e
/ / 2\\ d | 2 \x /| --\x *e / dx
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
Apply the power rule: goes to
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
/ 2\ / 2\ \x / 3 \x / 2*x*e + 2*x *e
/ 2\ / 2 2 / 2\\ \x / 2*\1 + 4*x + x *\1 + 2*x //*e
/ 2\ / 2 2 / 2\\ \x / 4*x*\6 + 6*x + x *\3 + 2*x //*e