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

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
xx+1\frac{x}{x + 1} 
x/(1 + x)
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)=xf{\left(x \right)} = x and g(x)=x+1g{\left(x \right)} = x + 1.

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

    1. Apply the power rule: xx goes to 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:

    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
02468-8-6-4-2-1010200-100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1        x    
----- - --------
1 + x          2
        (1 + x)
−x(x+1)2+1x+1- \frac{x}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}
Simplify
The second derivative [src] 
  /       x  \
2*|-1 + -----|
  \     1 + x/
--------------
          2   
   (1 + x)
2(xx+1−1)(x+1)2\frac{2 \left(\frac{x}{x + 1} - 1\right)}{\left(x + 1\right)^{2}}
Simplify
The third derivative [src] 
  /      x  \
6*|1 - -----|
  \    1 + x/
-------------
          3  
   (1 + x)
6(−xx+1+1)(x+1)3\frac{6 \left(- \frac{x}{x + 1} + 1\right)}{\left(x + 1\right)^{3}}
Simplify
The graph
Derivative of x/(1+x)
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