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Derivative of (x²-3x+3)/(x-1)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2          
x  - 3*x + 3
------------
   x - 1    
$$\frac{\left(x^{2} - 3 x\right) + 3}{x - 1}$$
(x^2 - 3*x + 3)/(x - 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      3. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
            2          
-3 + 2*x   x  - 3*x + 3
-------- - ------------
 x - 1              2  
             (x - 1)   
$$\frac{2 x - 3}{x - 1} - \frac{\left(x^{2} - 3 x\right) + 3}{\left(x - 1\right)^{2}}$$
The second derivative [src]
  /         2                 \
  |    3 + x  - 3*x   -3 + 2*x|
2*|1 + ------------ - --------|
  |             2      -1 + x |
  \     (-1 + x)              /
-------------------------------
             -1 + x            
$$\frac{2 \left(1 - \frac{2 x - 3}{x - 1} + \frac{x^{2} - 3 x + 3}{\left(x - 1\right)^{2}}\right)}{x - 1}$$
The third derivative [src]
  /                     2      \
  |     -3 + 2*x   3 + x  - 3*x|
6*|-1 + -------- - ------------|
  |      -1 + x             2  |
  \                 (-1 + x)   /
--------------------------------
                   2            
           (-1 + x)             
$$\frac{6 \left(-1 + \frac{2 x - 3}{x - 1} - \frac{x^{2} - 3 x + 3}{\left(x - 1\right)^{2}}\right)}{\left(x - 1\right)^{2}}$$