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Derivative of:
Derivative of u
Derivative of e^x/x^2
Derivative of cos(x)/x^2
Derivative of cos(sqrt(x))
How do you in partial fractions?:
1/(x-1)^2
Integral of d{x}:
1/(x-1)^2
Equation:
1/(x-1)^2
Identical expressions
one /(x- one)^ two
1 divide by (x minus 1) squared
one divide by (x minus one) to the power of two
1/(x-1)2
1/x-12
1/(x-1)²
1/(x-1) to the power of 2
1/x-1^2
1 divide by (x-1)^2
Similar expressions
1/(x+1)^2
-(e^(1/x-1))/((x-1)^2)

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

Derivative of 1/(x-1)^2

The solution

You have entered [src]

   1    
--------
       2
(x - 1)

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

1/((x - 1)^2)

Detail solution

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

$- \frac{2 x - 2}{\left(x - 1\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    6    
---------
        4
(-1 + x)

$$\frac{6}{\left(x - 1\right)^{4}}$$

Simplify

The third derivative [src]

   -24   
---------
        5
(-1 + x)

$$- \frac{24}{\left(x - 1\right)^{5}}$$

Simplify

The graph

Derivative of 1/(x-1)^2