log(x) - 1 ---------- 2 log (x)
(log(x) - 1)/log(x)^2
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 :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 2*(log(x) - 1) --------- - -------------- 2 3 x*log (x) x*log (x)
/ 3 \ 2*|1 + ------|*(-1 + log(x)) 4 \ log(x)/ -1 - ------ + ---------------------------- log(x) log(x) ------------------------------------------ 2 2 x *log (x)
/ / 9 12 \\ | / 3 \ (-1 + log(x))*|2 + ------ + -------|| | 3*|1 + ------| | log(x) 2 || | 3 \ log(x)/ \ log (x)/| 2*|1 + ------ + -------------- - ------------------------------------| \ log(x) log(x) log(x) / ---------------------------------------------------------------------- 3 2 x *log (x)