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

Derivative of 1/(x^2-2x)

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

The graph:

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The solution

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

  1. Let u=x2−2xu = x^{2} - 2 x.

  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(x2−2x)\frac{d}{d x} \left(x^{2} - 2 x\right):

    1. Differentiate x2−2xx^{2} - 2 x term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 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: −2-2

      The result is: 2x−22 x - 2

    The result of the chain rule is:

    −2x−2(x2−2x)2- \frac{2 x - 2}{\left(x^{2} - 2 x\right)^{2}}

  4. Now simplify:

    2(1−x)x2(x−2)2\frac{2 \left(1 - x\right)}{x^{2} \left(x - 2\right)^{2}}

The answer is:

2(1−x)x2(x−2)2\frac{2 \left(1 - x\right)}{x^{2} \left(x - 2\right)^{2}}

The graph
02468-8-6-4-2-1010-100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  2 - 2*x  
-----------
          2
/ 2      \ 
\x  - 2*x/
2−2x(x2−2x)2\frac{2 - 2 x}{\left(x^{2} - 2 x\right)^{2}}
Simplify
The second derivative [src] 
  /               2\
  |     4*(-1 + x) |
2*|-1 + -----------|
  \      x*(-2 + x)/
--------------------
     2         2    
    x *(-2 + x)
2(−1+4(x−1)2x(x−2))x2(x−2)2\frac{2 \left(-1 + \frac{4 \left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x^{2} \left(x - 2\right)^{2}}
Simplify
The third derivative [src] 
   /              2\         
   |    2*(-1 + x) |         
24*|1 - -----------|*(-1 + x)
   \     x*(-2 + x)/         
-----------------------------
          3         3        
         x *(-2 + x)
24(1−2(x−1)2x(x−2))(x−1)x3(x−2)3\frac{24 \left(1 - \frac{2 \left(x - 1\right)^{2}}{x \left(x - 2\right)}\right) \left(x - 1\right)}{x^{3} \left(x - 2\right)^{3}}
Simplify
The graph
Derivative of 1/(x^2-2x)
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