Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
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*x 2*x*\x + 1/ ------ - ------------ 2 2 x - 1 / 2 \ \x - 1/
/ / 2 \\ | / 2\ | 4*x || | \1 + x /*|-1 + -------|| | 2 | 2|| | 4*x \ -1 + x /| 2*|1 - ------- + -----------------------| | 2 2 | \ -1 + x -1 + x / ----------------------------------------- 2 -1 + x
/ / 2 \\ | / 2\ | 2*x || | 2*\1 + x /*|-1 + -------|| | 2 | 2|| | 4*x \ -1 + x /| 12*x*|-2 + ------- - -------------------------| | 2 2 | \ -1 + x -1 + x / ----------------------------------------------- 2 / 2\ \-1 + x /