4*x --------- 2 / 2 \ \x - 1/
(4*x)/(x^2 - 1)^2
Apply the quotient rule, which is:
and .
To find :
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:
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 4 16*x --------- - --------- 2 3 / 2 \ / 2 \ \x - 1/ \x - 1/
/ 2 \ | 6*x | 16*x*|-3 + -------| | 2| \ -1 + x / ------------------- 3 / 2\ \-1 + x /
/ / 2 \\ | 2 | 8*x || | 2*x *|-3 + -------|| | 2 | 2|| | 6*x \ -1 + x /| 48*|-1 + ------- - -------------------| | 2 2 | \ -1 + x -1 + x / --------------------------------------- 3 / 2\ \-1 + x /