2 x - 3*x + 3 ------------ x - 1
(x^2 - 3*x + 3)/(x - 1)
Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result 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:
2 -3 + 2*x x - 3*x + 3 -------- - ------------ x - 1 2 (x - 1)
/ 2 \ | 3 + x - 3*x -3 + 2*x| 2*|1 + ------------ - --------| | 2 -1 + x | \ (-1 + x) / ------------------------------- -1 + x