x ___ x*\/ e
d / 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 quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
1 - x x ___ e \/ e - -- x
1 - / 1 3\ x |- -- - -|*e | 2 x| \ x / ------------- 3 x