Differentiate term by term:
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:
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:
The result is:
Now simplify:
The answer is:
10 12*log (11 + x)*(11 - log(11 + x)) ----------------------------------- 2 (11 + x)
9 / 2 \ 12*log (11 + x)*\110 - 33*log(11 + x) + 2*log (11 + x)/ ------------------------------------------------------- 3 (11 + x)