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The derivative of the function/ 1/(x^2-9x+20)

Derivative of 1/(x^2-9x+20)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      1      
-------------
 2           
x  - 9*x + 20
$$\frac{1}{\left(x^{2} - 9 x\right) + 20}$$ 
1/(x^2 - 9*x + 20)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. 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:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    9 - 2*x     
----------------
               2
/ 2           \ 
\x  - 9*x + 20/
$$\frac{9 - 2 x}{\left(\left(x^{2} - 9 x\right) + 20\right)^{2}}$$
Simplify
The second derivative [src] 
  /                2 \
  |      (-9 + 2*x)  |
2*|-1 + -------------|
  |           2      |
  \     20 + x  - 9*x/
----------------------
                  2   
   /      2      \    
   \20 + x  - 9*x/
$$\frac{2 \left(\frac{\left(2 x - 9\right)^{2}}{x^{2} - 9 x + 20} - 1\right)}{\left(x^{2} - 9 x + 20\right)^{2}}$$
Simplify
The third derivative [src] 
             /               2 \
             |     (-9 + 2*x)  |
6*(-9 + 2*x)*|2 - -------------|
             |          2      |
             \    20 + x  - 9*x/
--------------------------------
                       3        
        /      2      \         
        \20 + x  - 9*x/
$$\frac{6 \left(2 x - 9\right) \left(- \frac{\left(2 x - 9\right)^{2}}{x^{2} - 9 x + 20} + 2\right)}{\left(x^{2} - 9 x + 20\right)^{3}}$$
Simplify
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