Apply the quotient rule, which is:
and .
To find :
The derivative of is .
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 log(x) --------- - -------- x*(x - 1) 2 (x - 1)
1 2 2*log(x) - -- - ---------- + --------- 2 x*(-1 + x) 2 x (-1 + x) ----------------------------- -1 + x
2 6*log(x) 3 6 -- - --------- + ----------- + ----------- 3 3 2 2 x (-1 + x) x *(-1 + x) x*(-1 + x) ------------------------------------------ -1 + x