x - 3 ----- x + 2
d /x - 3\ --|-----| dx\x + 2/
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:
The answer is:
1 x - 3 ----- - -------- x + 2 2 (x + 2)
/ -3 + x\ 2*|-1 + ------| \ 2 + x / --------------- 2 (2 + x)
/ -3 + x\ 6*|1 - ------| \ 2 + x / -------------- 3 (2 + x)