2 x - 1 ------- x*3 + 1
/ 2 \ d | x - 1| --|-------| dx\x*3 + 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.
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
/ 2 \ 3*\x - 1/ 2*x - ---------- + ------- 2 x*3 + 1 (x*3 + 1)
/ / 2\\ | 6*x 9*\-1 + x /| 2*|1 - ------- + -----------| | 1 + 3*x 2| \ (1 + 3*x) / ----------------------------- 1 + 3*x
/ / 2\ \ | 9*\-1 + x / 6*x | 18*|-1 - ----------- + -------| | 2 1 + 3*x| \ (1 + 3*x) / ------------------------------- 2 (1 + 3*x)