log(x) -------- 2 (x + 1)
log(x)/(x + 1)^2
Apply the quotient rule, which is:
and .
To find :
The derivative of 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:
1 (-2 - 2*x)*log(x) ---------- + ----------------- 2 4 x*(x + 1) (x + 1)
1 4 6*log(x) - -- - --------- + -------- 2 x*(1 + x) 2 x (1 + x) --------------------------- 2 (1 + x)
/1 12*log(x) 3 9 \ 2*|-- - --------- + ---------- + ----------| | 3 3 2 2| \x (1 + x) x *(1 + x) x*(1 + x) / -------------------------------------------- 2 (1 + x)