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Integral of d{x}:
1/(x^2-9x+20)
Identical expressions
one /(x^ two -9x+ twenty)
1 divide by (x squared minus 9x plus 20)
one divide by (x to the power of two minus 9x plus twenty)
1/(x2-9x+20)
1/x2-9x+20
1/(x²-9x+20)
1/(x to the power of 2-9x+20)
1/x^2-9x+20
1 divide by (x^2-9x+20)
Similar expressions
1/(x^2+9x+20)
1/(x^2-9x-20)

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

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

The solution

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      1      
-------------
 2           
x  - 9*x + 20

$$\frac{1}{\left(x^{2} - 9 x\right) + 20}$$

1/(x^2 - 9*x + 20)

Detail solution

Let $u = \left(x^{2} - 9 x\right) + 20$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} - 9 x\right) + 20\right)$ :
1. Differentiate $\left(x^{2} - 9 x\right) + 20$ term by term:
  1. Differentiate $x^{2} - 9 x$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. 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: $-9$
    The result is: $2 x - 9$
  2. The derivative of the constant $20$ is zero.
  The result is: $2 x - 9$
The result of the chain rule is:

$- \frac{2 x - 9}{\left(\left(x^{2} - 9 x\right) + 20\right)^{2}}$
Now simplify:

$\frac{9 - 2 x}{\left(x^{2} - 9 x + 20\right)^{2}}$

The answer is:

$\frac{9 - 2 x}{\left(x^{2} - 9 x + 20\right)^{2}}$

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

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