2 x + 289 -------- x
/ 2 \ d |x + 289| --|--------| dx\ 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:
/ 2\ | 289 + x | 2*|-1 + --------| | 2 | \ x / ----------------- x
/ 2\ | 289 + x | 6*|1 - --------| | 2 | \ x / ---------------- 2 x