Mister Exam

Derivative of x/(1+x)

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. Apply the power rule: goes to

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