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Derivative of:
Derivative of (-2)/x^2
Derivative of 2x^2-x
Derivative of (cos(x))^sin(x)
Derivative of y=3x^2
Graphing y =:
(x^2)/(x-1)
Integral of d{x}:
(x^2)/(x-1)
Identical expressions
(x^ two)/(x- one)
(x squared ) divide by (x minus 1)
(x to the power of two) divide by (x minus one)
(x2)/(x-1)
x2/x-1
(x²)/(x-1)
(x to the power of 2)/(x-1)
x^2/x-1
(x^2) divide by (x-1)
Similar expressions
(x^2)/(x+1)

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

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

The solution

You have entered [src]

   2 
  x  
-----
x - 1

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

x^2/(x - 1)

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
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:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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

The graph:

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The solution