Apply the quotient rule, which is:
and .
To find :
The derivative of is itself.
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
x x e 2*x*e ------ - --------- 2 2 x + 1 / 2 \ \x + 1/
/ / 2 \\ | | 4*x || | 2*|-1 + ------|| | | 2|| | 4*x \ 1 + x /| x |1 - ------ + ---------------|*e | 2 2 | \ 1 + x 1 + x / --------------------------------- 2 1 + x
/ / 2 \ / 2 \\ | | 4*x | | 2*x || | 6*|-1 + ------| 24*x*|-1 + ------|| | | 2| | 2|| | 6*x \ 1 + x / \ 1 + x /| x |1 - ------ + --------------- - ------------------|*e | 2 2 2 | | 1 + x 1 + x / 2\ | \ \1 + x / / ------------------------------------------------------ 2 1 + x