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Derivative of:
Derivative of z
Derivative of x^5*cos(x)
Derivative of x^(3/4)
Derivative of (x-1)/(x+1)
Graphing y =:
(x-1)/(x+1)
Integral of d{x}:
(x-1)/(x+1)
Canonical form:
(x-1)/(x+1)
Identical expressions
(x- one)/(x+ one)
(x minus 1) divide by (x plus 1)
(x minus one) divide by (x plus one)
x-1/x+1
(x-1) divide by (x+1)
Similar expressions
(x+1)/(x+1)
(x-1)/(x-1)

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

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

The solution

You have entered [src]

x - 1
-----
x + 1

$$\frac{x - 1}{x + 1}$$

d /x - 1\
--|-----|
dx\x + 1/

$$\frac{d}{d x} \frac{x - 1}{x + 1}$$

Transform

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x - 1$ and $g{\left(x \right)} = x + 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x - 1$ term by term:
  1. The derivative of the constant $-1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /     -1 + x\
2*|-1 + ------|
  \     1 + x /
---------------
           2   
    (1 + x)

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

Simplify

The third derivative [src]

  /    -1 + x\
6*|1 - ------|
  \    1 + x /
--------------
          3   
   (1 + x)

$$\frac{6 \left(- \frac{x - 1}{x + 1} + 1\right)}{\left(x + 1\right)^{3}}$$

Simplify

The graph

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