Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of is .
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:
/ 2 \ 4*x*log\x + 1/ --------------- 2 x + 1
/ 2 2 / 2\ \ | 2*x 2*x *log\1 + x / / 2\| 4*|------ - ---------------- + log\1 + x /| | 2 2 | \1 + x 1 + x / ------------------------------------------- 2 1 + x
/ 2 2 / 2\\ | / 2\ 6*x 4*x *log\1 + x /| 8*x*|3 - 3*log\1 + x / - ------ + ----------------| | 2 2 | \ 1 + x 1 + x / --------------------------------------------------- 2 / 2\ \1 + x /