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:
___ ___ \/ x \/ x e e ------ + ------- 2 ___ 2*\/ x
___ / 1 2 ___ /1 1 \\ \/ x |- ---- + - + \/ x *|- - ----||*e | 3/2 x |x 3/2|| \ x \ x // -------------------------------------- 4
/ /1 1 \\ | 3*|- - ----|| | |x 3/2|| ___ | 3 3 ___ / 1 3 3 \ \ x /| \/ x |- -- + ---- + \/ x *|---- - -- + ----| + ------------|*e | 2 5/2 | 3/2 2 5/2| ___ | \ x x \x x x / \/ x / -------------------------------------------------------------- 8