1 1*------ 3 x + 1
d / 1 \ --|1*------| dx| 3 | \ x + 1/
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
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:
The answer is:
2 -3*x --------- 2 / 3 \ \x + 1/
/ 3 \ | 3*x | 6*x*|-1 + ------| | 3| \ 1 + x / ----------------- 2 / 3\ \1 + x /
/ 3 6 \ | 18*x 27*x | -6*|1 - ------ + ---------| | 3 2| | 1 + x / 3\ | \ \1 + x / / --------------------------- 2 / 3\ \1 + x /