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

Derivative of 1/(x^2-3*x+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
       1      
1*------------
   2          
  x  - 3*x + 2
$$1 \cdot \frac{1}{x^{2} - 3 x + 2}$$
d /       1      \
--|1*------------|
dx|   2          |
  \  x  - 3*x + 2/
$$\frac{d}{d x} 1 \cdot \frac{1}{x^{2} - 3 x + 2}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of the constant is zero.

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