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

Derivative of 1/(x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1  
-----
x - 1
1x−1\frac{1}{x - 1} 
1/(x - 1)
Detail solution

  1. Let u=x−1u = x - 1.

  2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddx(x−1)\frac{d}{d x} \left(x - 1\right):

    1. Differentiate x−1x - 1 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant −1-1 is zero.

      The result is: 11

    The result of the chain rule is:

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

  4. Now simplify:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-200100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  -1    
--------
       2
(x - 1)
−1(x−1)2- \frac{1}{\left(x - 1\right)^{2}}
Simplify
The second derivative [src] 
    2    
---------
        3
(-1 + x)
2(x−1)3\frac{2}{\left(x - 1\right)^{3}}
Simplify
The third derivative [src] 
   -6    
---------
        4
(-1 + x)
−6(x−1)4- \frac{6}{\left(x - 1\right)^{4}}
Simplify
The graph
Derivative of 1/(x-1)
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