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The derivative of the function/ x/(x^2+9)

Derivative of x/(x^2+9)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x   
------
 2    
x  + 9
$$\frac{x}{x^{2} + 9}$$ 
x/(x^2 + 9)
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
               2  
  1         2*x   
------ - ---------
 2               2
x  + 9   / 2    \ 
         \x  + 9/
$$- \frac{2 x^{2}}{\left(x^{2} + 9\right)^{2}} + \frac{1}{x^{2} + 9}$$
Simplify
The second derivative [src] 
    /         2 \
    |      4*x  |
2*x*|-3 + ------|
    |          2|
    \     9 + x /
-----------------
            2    
    /     2\     
    \9 + x /
$$\frac{2 x \left(\frac{4 x^{2}}{x^{2} + 9} - 3\right)}{\left(x^{2} + 9\right)^{2}}$$
Simplify
The third derivative [src] 
  /                   /         2 \\
  |                 2 |      2*x  ||
  |              4*x *|-1 + ------||
  |         2         |          2||
  |      4*x          \     9 + x /|
6*|-1 + ------ - ------------------|
  |          2              2      |
  \     9 + x          9 + x       /
------------------------------------
                     2              
             /     2\               
             \9 + x /
$$\frac{6 \left(- \frac{4 x^{2} \left(\frac{2 x^{2}}{x^{2} + 9} - 1\right)}{x^{2} + 9} + \frac{4 x^{2}}{x^{2} + 9} - 1\right)}{\left(x^{2} + 9\right)^{2}}$$
Simplify
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