2 x - 9 ------ x + 3
/ 2 \ d |x - 9| --|------| dx\x + 3 /
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 x - 9 2*x - -------- + ----- 2 x + 3 (x + 3)
/ 2 \ | -9 + x 2*x | 2*|1 + -------- - -----| | 2 3 + x| \ (3 + x) / ------------------------ 3 + x