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Derivative of x/(x^2-3x+2)

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. Apply the power rule: goes to

    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:

    Now plug in to the quotient rule:


The answer is:

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