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The derivative of the function/ 3/(x^2+1)

Derivative of 3/(x^2+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3   
------
 2    
x  + 1
$$\frac{3}{x^{2} + 1}$$ 
3/(x^2 + 1)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   -6*x  
---------
        2
/ 2    \ 
\x  + 1/
$$- \frac{6 x}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The second derivative [src] 
  /         2 \
  |      4*x  |
6*|-1 + ------|
  |          2|
  \     1 + x /
---------------
           2   
   /     2\    
   \1 + x /
$$\frac{6 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
      /         2 \
      |      2*x  |
-72*x*|-1 + ------|
      |          2|
      \     1 + x /
-------------------
             3     
     /     2\      
     \1 + x /
$$- \frac{72 x \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{3}}$$
Simplify
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