3 x + 4 ------ 2 x
/ 3 \ d |x + 4| --|------| dx| 2 | \ x /
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 :
Apply the power rule: goes to
Now plug in to the quotient rule:
Now simplify:
The answer is:
/ 3 \ 2 2*\x + 4/ 3*x - ---------- + ---- 3 2 x x
/ 3\ | 4 + x | 6*|-1 + ------| | 3 | \ x / --------------- x
/ 3\ | 4 + x | 24*|1 - ------| | 3 | \ x / --------------- 2 x