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Graphing y =:
x/(x^2-3x+2)
Integral of d{x}:
x/(x^2-3x+2)
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x/(x^ two -3x+ two)
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x/x^2-3x+2
x divide by (x^2-3x+2)
Similar expressions
x/(x^2-3x-2)
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The derivative of the function/ x/(x^2-3x+2)

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

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

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x$ and $g{\left(x \right)} = x^{2} - 3 x + 2$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} - 3 x + 2$ term by term:
  1. The derivative of the constant $2$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  3. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $-3$
  The result is: $2 x - 3$
Now plug in to the quotient rule:

$\frac{x^{2} - x \left(2 x - 3\right) - 3 x + 2}{\left(x^{2} - 3 x + 2\right)^{2}}$

The answer is:

$\frac{x^{2} - x \left(2 x - 3\right) - 3 x + 2}{\left(x^{2} - 3 x + 2\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     1           x*(3 - 2*x)  
------------ + ---------------
 2                           2
x  - 3*x + 2   / 2          \ 
               \x  - 3*x + 2/

$$\frac{x \left(3 - 2 x\right)}{\left(\left(x^{2} - 3 x\right) + 2\right)^{2}} + \frac{1}{\left(x^{2} - 3 x\right) + 2}$$

Simplify

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/

$$\frac{2 \left(x \left(\frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x + 2} - 1\right) - 2 x + 3\right)}{\left(x^{2} - 3 x + 2\right)^{2}}$$

Simplify

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/

$$\frac{6 \left(- \frac{x \left(2 x - 3\right) \left(\frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x + 2} - 2\right)}{x^{2} - 3 x + 2} + \frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x + 2} - 1\right)}{\left(x^{2} - 3 x + 2\right)^{2}}$$

Simplify

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

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The solution