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Derivative of:
Derivative of x^(-2)
Derivative of (x^2-1)^3
Derivative of sqrt(1/x)
Derivative of sin(x)^(9)
Graphing y =:
x/(x+1)^2
Integral of d{x}:
x/(x+1)^2
Identical expressions
x/(x+ one)^ two
x divide by (x plus 1) squared
x divide by (x plus one) to the power of two
x/(x+1)2
x/x+12
x/(x+1)²
x/(x+1) to the power of 2
x/x+1^2
x divide by (x+1)^2
Similar expressions
x/(x-1)^2

The derivative of the function/ x/(x+1)^2

Derivative of x/(x+1)^2

The solution

You have entered [src]

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

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

x/(x + 1)^2

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x$ and $g{\left(x \right)} = \left(x + 1\right)^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = x + 1$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)$ :
  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: $1$
  The result of the chain rule is:
  
  $2 x + 2$
Now plug in to the quotient rule:

$\frac{- x \left(2 x + 2\right) + \left(x + 1\right)^{2}}{\left(x + 1\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1       x*(-2 - 2*x)
-------- + ------------
       2            4  
(x + 1)      (x + 1)

$$\frac{x \left(- 2 x - 2\right)}{\left(x + 1\right)^{4}} + \frac{1}{\left(x + 1\right)^{2}}$$

Simplify

The second derivative [src]

  /      3*x \
2*|-2 + -----|
  \     1 + x/
--------------
          3   
   (1 + x)

$$\frac{2 \left(\frac{3 x}{x + 1} - 2\right)}{\left(x + 1\right)^{3}}$$

Simplify

The third derivative [src]

  /     4*x \
6*|3 - -----|
  \    1 + x/
-------------
          4  
   (1 + x)

$$\frac{6 \left(- \frac{4 x}{x + 1} + 3\right)}{\left(x + 1\right)^{4}}$$

Simplify

The graph

Derivative of x/(x+1)^2