x + 3 ----- x + 1
d /x + 3\ --|-----| dx\x + 1/
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 + 1 2 (x + 1)
/ 3 + x\ 2*|-1 + -----| \ 1 + x/ -------------- 2 (1 + x)
/ 3 + x\ 6*|1 - -----| \ 1 + x/ ------------- 3 (1 + x)