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Integral of d{x}:
1/(2x^2-5x+7)
Identical expressions
one /(two x^2-5x+ seven)
1 divide by (2x squared minus 5x plus 7)
one divide by (two x squared minus 5x plus seven)
1/(2x2-5x+7)
1/2x2-5x+7
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1/(2x to the power of 2-5x+7)
1/2x^2-5x+7
1 divide by (2x^2-5x+7)
Similar expressions
1/(2x^2+5x+7)
1/(2x^2-5x-7)

The derivative of the function/ 1/(2x^2-5x+7)

Derivative of 1/(2x^2-5x+7)

The solution

You have entered [src]

      1       
--------------
   2          
2*x  - 5*x + 7

$$\frac{1}{\left(2 x^{2} - 5 x\right) + 7}$$

1/(2*x^2 - 5*x + 7)

Detail solution

Let $u = \left(2 x^{2} - 5 x\right) + 7$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(2 x^{2} - 5 x\right) + 7\right)$ :
1. Differentiate $\left(2 x^{2} - 5 x\right) + 7$ term by term:
  1. Differentiate $2 x^{2} - 5 x$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      So, the result is: $4 x$
    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: $-5$
    The result is: $4 x - 5$
  2. The derivative of the constant $7$ is zero.
  The result is: $4 x - 5$
The result of the chain rule is:

$- \frac{4 x - 5}{\left(\left(2 x^{2} - 5 x\right) + 7\right)^{2}}$
Now simplify:

$\frac{5 - 4 x}{\left(2 x^{2} - 5 x + 7\right)^{2}}$

The answer is:

$\frac{5 - 4 x}{\left(2 x^{2} - 5 x + 7\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     5 - 4*x     
-----------------
                2
/   2          \ 
\2*x  - 5*x + 7/

$$\frac{5 - 4 x}{\left(\left(2 x^{2} - 5 x\right) + 7\right)^{2}}$$

Simplify

The second derivative [src]

  /                2  \
  |      (-5 + 4*x)   |
2*|-2 + --------------|
  |                  2|
  \     7 - 5*x + 2*x /
-----------------------
                   2   
   /             2\    
   \7 - 5*x + 2*x /

$$\frac{2 \left(\frac{\left(4 x - 5\right)^{2}}{2 x^{2} - 5 x + 7} - 2\right)}{\left(2 x^{2} - 5 x + 7\right)^{2}}$$

Simplify

The third derivative [src]

             /               2  \
             |     (-5 + 4*x)   |
6*(-5 + 4*x)*|4 - --------------|
             |                 2|
             \    7 - 5*x + 2*x /
---------------------------------
                        3        
        /             2\         
        \7 - 5*x + 2*x /

$$\frac{6 \left(4 x - 5\right) \left(- \frac{\left(4 x - 5\right)^{2}}{2 x^{2} - 5 x + 7} + 4\right)}{\left(2 x^{2} - 5 x + 7\right)^{3}}$$

Simplify

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Derivative of 1/(2x^2-5x+7)

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The solution