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1/(x-1)^2

Derivative of 1/(x-1)^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   1    
--------
       2
(x - 1) 
$$\frac{1}{\left(x - 1\right)^{2}}$$
1/((x - 1)^2)
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
     2 - 2*x     
-----------------
       2        2
(x - 1) *(x - 1) 
$$\frac{2 - 2 x}{\left(x - 1\right)^{2} \left(x - 1\right)^{2}}$$
The second derivative [src]
    6    
---------
        4
(-1 + x) 
$$\frac{6}{\left(x - 1\right)^{4}}$$
The third derivative [src]
   -24   
---------
        5
(-1 + x) 
$$- \frac{24}{\left(x - 1\right)^{5}}$$
The graph
Derivative of 1/(x-1)^2