n / 2 \ \x - 1/
/ n\ d |/ 2 \ | --\\x - 1/ / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
n / 2 \ 2*n*x*\x - 1/ --------------- 2 x - 1
n / 2 2\ / 2\ | 2*x 2*n*x | 2*n*\-1 + x / *|1 - ------- + -------| | 2 2| \ -1 + x -1 + x / -------------------------------------- 2 -1 + x
n / 2 2 2 2\ / 2\ | 4*x 6*n*x 2*n *x | 4*n*x*\-1 + x / *|-3 + 3*n + ------- - ------- + -------| | 2 2 2| \ -1 + x -1 + x -1 + x / --------------------------------------------------------- 2 / 2\ \-1 + x /