Mister Exam

Other calculators

(x-1)/(x+1)
The derivative of the function/ (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
x−1x+1\frac{x - 1}{x + 1} 
d /x - 1\
--|-----|
dx\x + 1/
ddxx−1x+1\frac{d}{d x} \frac{x - 1}{x + 1}
Transform
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\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(x)=x−1f{\left(x \right)} = x - 1 and g(x)=x+1g{\left(x \right)} = x + 1.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

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

      2. Apply the power rule: xx goes to 11

      The result is: 11

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate x+1x + 1 term by term:

      1. The derivative of the constant 11 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1      x - 1  
----- - --------
x + 1          2
        (x + 1)
1x+1−x−1(x+1)2\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)
2(x−1x+1−1)(x+1)2\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)
6(−x−1x+1+1)(x+1)3\frac{6 \left(- \frac{x - 1}{x + 1} + 1\right)}{\left(x + 1\right)^{3}}
Simplify
The graph
Derivative of (x-1)/(x+1)
    © Mister Exam – Calculator