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Integral of d{x}:
1/(x^2-2x)
Graphing y =:
1/(x^2-2x)
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one /(x^ two -2x)
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Similar expressions
1/(x^2+2x)

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

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

The solution

You have entered [src]

   1    
--------
 2      
x  - 2*x

$$\frac{1}{x^{2} - 2 x}$$

1/(x^2 - 2*x)

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2 - 2*x  
-----------
          2
/ 2      \ 
\x  - 2*x/

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

Simplify

The second derivative [src]

  /               2\
  |     4*(-1 + x) |
2*|-1 + -----------|
  \      x*(-2 + x)/
--------------------
     2         2    
    x *(-2 + x)

$$\frac{2 \left(-1 + \frac{4 \left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x^{2} \left(x - 2\right)^{2}}$$

Simplify

The third derivative [src]

   /              2\         
   |    2*(-1 + x) |         
24*|1 - -----------|*(-1 + x)
   \     x*(-2 + x)/         
-----------------------------
          3         3        
         x *(-2 + x)

$$\frac{24 \left(1 - \frac{2 \left(x - 1\right)^{2}}{x \left(x - 2\right)}\right) \left(x - 1\right)}{x^{3} \left(x - 2\right)^{3}}$$

Simplify

The graph

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

The graph:

Piecewise:

The solution