Apply the quotient rule, which is:
and .
To find :
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:
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:
2 2 4*x ------ - --------- 2 2 x + 1 / 2 \ \x + 1/
/ 2 \ | 4*x | 4*x*|-3 + ------| | 2| \ 1 + x / ----------------- 2 / 2\ \1 + x /
/ / 2 \\ | 2 | 2*x || | 4*x *|-1 + ------|| | 2 | 2|| | 4*x \ 1 + x /| 12*|-1 + ------ - ------------------| | 2 2 | \ 1 + x 1 + x / ------------------------------------- 2 / 2\ \1 + x /