log(x + 1) ---------- 2 x
log(x + 1)/x^2
Apply the quotient rule, which is:
and .
To find :
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:
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 2*log(x + 1) ---------- - ------------ 2 3 x *(x + 1) x
1 4 6*log(1 + x) - -------- - --------- + ------------ 2 x*(1 + x) 2 (1 + x) x ------------------------------------- 2 x
/ 1 12*log(1 + x) 3 9 \ 2*|-------- - ------------- + ---------- + ----------| | 3 3 2 2 | \(1 + x) x x*(1 + x) x *(1 + x)/ ------------------------------------------------------ 2 x