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(x-1)/(x+1)

Derivative of (x-1)/(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x - 1
-----
x + 1
$$\frac{x - 1}{x + 1}$$
d /x - 1\
--|-----|
dx\x + 1/
$$\frac{d}{d x} \frac{x - 1}{x + 1}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
  1      x - 1  
----- - --------
x + 1          2
        (x + 1) 
$$\frac{1}{x + 1} - \frac{x - 1}{\left(x + 1\right)^{2}}$$
The second derivative [src]
  /     -1 + x\
2*|-1 + ------|
  \     1 + x /
---------------
           2   
    (1 + x)    
$$\frac{2 \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x + 1\right)^{2}}$$
The third derivative [src]
  /    -1 + x\
6*|1 - ------|
  \    1 + x /
--------------
          3   
   (1 + x)    
$$\frac{6 \left(- \frac{x - 1}{x + 1} + 1\right)}{\left(x + 1\right)^{3}}$$
The graph
Derivative of (x-1)/(x+1)