x^2*e^(3*x)
2 3*x x *e
d / 2 3*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 :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
/ 2 \ 3*x \2 + 9*x + 12*x/*e
/ 2 \ 3*x 9*\2 + 3*x + 6*x/*e