3 x -------- 2 (x - 1)
x^3/(x - 1)^2
Apply the quotient rule, which is:
and .
To find :
Apply the power rule: goes to
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:
2 3 3*x x *(2 - 2*x) -------- + ------------ 2 4 (x - 1) (x - 1)
/ 2 \ | x 2*x | 6*x*|1 + --------- - ------| | 2 -1 + x| \ (-1 + x) / ---------------------------- 2 (-1 + x)
/ 3 2 \ | 6*x 4*x 9*x | 6*|1 - ------ - --------- + ---------| | -1 + x 3 2| \ (-1 + x) (-1 + x) / -------------------------------------- 2 (-1 + x)