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Derivative of:
Derivative of x^4*e^x
Derivative of 5^-x
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Derivative of x^2/cosx
Integral of d{x}:
4*x/(1+x^2)
Graphing y =:
4*x/(1+x^2)
Limit of the function:
4*x/(1+x^2)
Identical expressions
four *x/(one +x^ two)
4 multiply by x divide by (1 plus x squared )
four multiply by x divide by (one plus x to the power of two)
4*x/(1+x2)
4*x/1+x2
4*x/(1+x²)
4*x/(1+x to the power of 2)
4x/(1+x^2)
4x/(1+x2)
4x/1+x2
4x/1+x^2
4*x divide by (1+x^2)
Similar expressions
4*x/(1-x^2)
What you mean?
4*x/(1 + x^2)
4*x*2/(1 + x)
4*x/((1 + x)^2)
4*x/1 + x^2
4*x/(1 + x^2)
4*x*2/(1 + x)
4*x/1 + x^2

The derivative of the function/ 4*x/(1+x^2)

You entered:

4*x/(1+x^2)

What you mean?

4*x/(1 + x^2)

4*x*2/(1 + x)

4*x/((1 + x)^2)

4*x/1 + x^2

4*x/(1 + x^2)

4*x*2/(1 + x)

4*x/1 + x^2

Derivative of 4*x/(1+x^2)

The solution

You have entered [src]

 4*x  
------
     2
1 + x

$$\frac{4 x}{x^{2} + 1}$$

d / 4*x  \
--|------|
dx|     2|
  \1 + x /

$$\frac{d}{d x} \frac{4 x}{x^{2} + 1}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. 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 $g{\left(x \right)} = x^{2} + 1$ .
  
  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. Differentiate $x^{2} + 1$ term by term:
    1. The derivative of the constant $1$ is zero.
    2. Apply the power rule: $x^{2}$ goes to $2 x$
    The result is: $2 x$
  Now plug in to the quotient rule:
  
  $\frac{1 - x^{2}}{\left(x^{2} + 1\right)^{2}}$
So, the result is: $\frac{4 \cdot \left(1 - x^{2}\right)}{\left(x^{2} + 1\right)^{2}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               2  
  4         8*x   
------ - ---------
     2           2
1 + x    /     2\ 
         \1 + x /

$$- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{4}{x^{2} + 1}$$

Simplify

The second derivative [src]

    /         2 \
    |      4*x  |
8*x*|-3 + ------|
    |          2|
    \     1 + x /
-----------------
            2    
    /     2\     
    \1 + x /

$$\frac{8 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}}$$

Simplify

The third derivative [src]

   /                   /         2 \\
   |                 2 |      2*x  ||
   |              4*x *|-1 + ------||
   |         2         |          2||
   |      4*x          \     1 + x /|
24*|-1 + ------ - ------------------|
   |          2              2      |
   \     1 + x          1 + x       /
-------------------------------------
                      2              
              /     2\               
              \1 + x /

$$\frac{24 \left(- \frac{4 x^{2} \cdot \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}$$

Simplify

The graph

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Identical expressions

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You entered:

What you mean?

Derivative of 4*x/(1+x^2)

The graph:

Piecewise:

The solution