ax^2e^(-x/2)
-x --- 2 2 a*x *e
/ -x \ | ---| d | 2 2 | --\a*x *e / dx
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the product rule:
; 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.
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:
So, the result is:
The result of the chain rule is:
; to find :
Apply the power rule: goes to
The result is:
So, the result is:
Now simplify:
The answer is:
-x -x --- --- 2 2 2 a*x *e 2*a*x*e - --------- 2
-x / 2\ --- | x | 2 a*|2 - 2*x + --|*e \ 4 /