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