log(x) - 1 ---------- log(x) + 1
(log(x) - 1)/(log(x) + 1)
Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
The derivative of is .
The result is:
To find :
Differentiate term by term:
The derivative of the constant is zero.
The derivative of is .
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 log(x) - 1 -------------- - --------------- x*(log(x) + 1) 2 x*(log(x) + 1)
/ 2 \ |1 + ----------|*(-1 + log(x)) 2 \ 1 + log(x)/ -1 - ---------- + ------------------------------ 1 + log(x) 1 + log(x) ------------------------------------------------ 2 x *(1 + log(x))
/ 3 3 \ / 2 \ 2*(-1 + log(x))*|1 + ---------- + -------------| 3*|1 + ----------| | 1 + log(x) 2| 3 \ 1 + log(x)/ \ (1 + log(x)) / 2 + ---------- + ------------------ - ------------------------------------------------ 1 + log(x) 1 + log(x) 1 + log(x) -------------------------------------------------------------------------------------- 3 x *(1 + log(x))