Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
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 plug in to the quotient rule:
Now simplify:
The answer is:
___ ___ -\/ x -\/ x e e - ------- - ------------- 3/2 ___ ___ 2*x 2*\/ x *\/ x
/ 1 1 \ | - + ----| | x 3/2| ___ |2 3 x | -\/ x |-- + ---- + --------|*e | 2 5/2 ___ | \x x \/ x / ------------------------------ 4
/ 1 6 15 15 / 1 3 3 \ /1 1 \\ | -- + ---- + -- + ---- 4*|---- + -- + ----| 18*|- + ----|| | 2 5/2 3 7/2 | 3/2 2 5/2| |x 3/2|| ___ |60 105 x x x x \x x x / \ x /| -\/ x |-- + ---- + --------------------- + -------------------- + -------------|*e | 4 9/2 ___ 3/2 5/2 | \x x \/ x x x / ---------------------------------------------------------------------------------- 16
/ 1 3 3 /1 1 \\ | ---- + -- + ---- 3*|- + ----|| | 3/2 2 5/2 |x 3/2|| ___ |9 15 x x x \ x /| -\/ x -|-- + ---- + ---------------- + ------------|*e | 3 7/2 ___ 3/2 | \x x \/ x x / ------------------------------------------------------- 8