Mister Exam

Other calculators

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

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      1       
--------------
   2          
2*x  - 5*x + 7
1(2x2−5x)+7\frac{1}{\left(2 x^{2} - 5 x\right) + 7} 
1/(2*x^2 - 5*x + 7)
Detail solution

  1. Let u=(2x2−5x)+7u = \left(2 x^{2} - 5 x\right) + 7.

  2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddx((2x2−5x)+7)\frac{d}{d x} \left(\left(2 x^{2} - 5 x\right) + 7\right):

    1. Differentiate (2x2−5x)+7\left(2 x^{2} - 5 x\right) + 7 term by term:

      1. Differentiate 2x2−5x2 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: x2x^{2} goes to 2x2 x

          So, the result is: 4x4 x

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: xx goes to 11

          So, the result is: −5-5

        The result is: 4x−54 x - 5

      2. The derivative of the constant 77 is zero.

      The result is: 4x−54 x - 5

    The result of the chain rule is:

    −4x−5((2x2−5x)+7)2- \frac{4 x - 5}{\left(\left(2 x^{2} - 5 x\right) + 7\right)^{2}}

  4. Now simplify:

    5−4x(2x2−5x+7)2\frac{5 - 4 x}{\left(2 x^{2} - 5 x + 7\right)^{2}}

The answer is:

5−4x(2x2−5x+7)2\frac{5 - 4 x}{\left(2 x^{2} - 5 x + 7\right)^{2}}

The graph
02468-8-6-4-2-10100.5-0.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     5 - 4*x     
-----------------
                2
/   2          \ 
\2*x  - 5*x + 7/
5−4x((2x2−5x)+7)2\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 /
2((4x−5)22x2−5x+7−2)(2x2−5x+7)2\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 /
6(4x−5)(−(4x−5)22x2−5x+7+4)(2x2−5x+7)3\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
    © Mister Exam – Calculator