1 --------- 7 / 2 \ \x - 1/
1/((x^2 - 1)^7)
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
Now simplify:
The answer is:
-14*x ------------------ 7 / 2 \ / 2 \ \x - 1/*\x - 1/
/ 2 \ | 16*x | 14*|-1 + -------| | 2| \ -1 + x / ----------------- 8 / 2\ \-1 + x /
/ 2 \ | 6*x | 672*x*|1 - -------| | 2| \ -1 + x / ------------------- 9 / 2\ \-1 + x /