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x^2/(x-1)^2

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    2   
   x    
--------
       2
(x - 1) 
$$\frac{x^{2}}{\left(x - 1\right)^{2}}$$
x^2/(x - 1)^2
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
            2          
  2*x      x *(2 - 2*x)
-------- + ------------
       2            4  
(x - 1)      (x - 1)   
$$\frac{x^{2} \left(2 - 2 x\right)}{\left(x - 1\right)^{4}} + \frac{2 x}{\left(x - 1\right)^{2}}$$
The second derivative [src]
  /                   2  \
  |     4*x        3*x   |
2*|1 - ------ + ---------|
  |    -1 + x           2|
  \             (-1 + x) /
--------------------------
                2         
        (-1 + x)          
$$\frac{2 \left(\frac{3 x^{2}}{\left(x - 1\right)^{2}} - \frac{4 x}{x - 1} + 1\right)}{\left(x - 1\right)^{2}}$$
The third derivative [src]
   /           2           \
   |        2*x       3*x  |
12*|-1 - --------- + ------|
   |             2   -1 + x|
   \     (-1 + x)          /
----------------------------
                 3          
         (-1 + x)           
$$\frac{12 \left(- \frac{2 x^{2}}{\left(x - 1\right)^{2}} + \frac{3 x}{x - 1} - 1\right)}{\left(x - 1\right)^{3}}$$
The graph
Derivative of x^2/(x-1)^2