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 \ 2*x 3*x *\x + 1/ ------ - ------------- 3 2 x + 1 / 3 \ \x + 1/
/ / 3 \\ | / 2\ | 3*x || | 3*x*\1 + x /*|-1 + ------|| | 3 | 3|| | 6*x \ 1 + x /| 2*|1 - ------ + --------------------------| | 3 3 | \ 1 + x 1 + x / ------------------------------------------- 3 1 + x
/ / 3 6 \ / 3 \\ | 2 / 2\ | 18*x 27*x | 2 | 3*x || 6*|- 3*x - \1 + x /*|1 - ------ + ---------| + 6*x *|-1 + ------|| | | 3 2| | 3|| | | 1 + x / 3\ | \ 1 + x /| \ \ \1 + x / / / ------------------------------------------------------------------- 2 / 3\ \1 + x /
/ / 3 6 \ / 3 \\ | 2 / 2\ | 18*x 27*x | 2 | 3*x || 6*|- 3*x - \1 + x /*|1 - ------ + ---------| + 6*x *|-1 + ------|| | | 3 2| | 3|| | | 1 + x / 3\ | \ 1 + x /| \ \ \1 + x / / / ------------------------------------------------------------------- 2 / 3\ \1 + x /