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Derivative of:
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Derivative of -1/(x-1)^2
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How do you in partial fractions?:
-1/(x-1)^2
Identical expressions
- one /(x- one)^ two
minus 1 divide by (x minus 1) squared
minus 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
-(e^(1/x-1))/((x-1)^2)
-1/(x+1)^2
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

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(x - 1\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. 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:
  
  $- \frac{2 x - 2}{\left(x - 1\right)^{4}}$
So, the result is: $\frac{2 x - 2}{\left(x - 1\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-(2 - 2*x) 
-----------
         4 
  (x - 1)

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

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