1 --------- 2 / 2\ \1 + x /
1/((1 + x^2)^2)
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:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
-4*x ------------------ 2 / 2\ / 2\ \1 + x /*\1 + x /
/ 2 \ | 6*x | 4*|-1 + ------| | 2| \ 1 + x / --------------- 3 / 2\ \1 + x /
/ 2 \ | 8*x | 24*x*|3 - ------| | 2| \ 1 + x / ----------------- 4 / 2\ \1 + x /