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(x^2-2*x)/(x-1)

How to use it?
Derivative of:
Derivative of x*ctgx
Derivative of x-cos(x)
Derivative of lnx^2
Derivative of ln(x)^2
Graphing y =:
(x^2-2*x)/(x-1)
Identical expressions
(x^ two - two *x)/(x- one)
(x squared minus 2 multiply by x) divide by (x minus 1)
(x to the power of two minus two multiply by x) divide by (x minus one)
(x2-2*x)/(x-1)
x2-2*x/x-1
(x²-2*x)/(x-1)
(x to the power of 2-2*x)/(x-1)
(x^2-2x)/(x-1)
(x2-2x)/(x-1)
x2-2x/x-1
x^2-2x/x-1
(x^2-2*x) divide by (x-1)
Similar expressions
(x^2+2*x)/(x-1)
(x^2-2*x)/(x+1)

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

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

The solution

You have entered [src]

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

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

  / 2      \
d |x  - 2*x|
--|--------|
dx\ x - 1  /

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

Transform

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2} - 2 x$ and $g{\left(x \right)} = x - 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
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: $2 x - 2$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 1$ term by term:
  1. The derivative of the constant $-1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{- x^{2} + 2 x + \left(x - 1\right) \left(2 x - 2\right)}{\left(x - 1\right)^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2      
-2 + 2*x   x  - 2*x
-------- - --------
 x - 1            2
           (x - 1)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /    x*(-2 + x)\
6*|1 - ----------|
  |            2 |
  \    (-1 + x)  /
------------------
            2     
    (-1 + x)

$$\frac{6 \left(- \frac{x \left(x - 2\right)}{\left(x - 1\right)^{2}} + 1\right)}{\left(x - 1\right)^{2}}$$

Simplify

The graph

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