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x/(9-x^2)

Derivative of x/(9-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  x   
------
     2
9 - x 
$$\frac{x}{9 - x^{2}}$$
x/(9 - x^2)
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
               2  
  1         2*x   
------ + ---------
     2           2
9 - x    /     2\ 
         \9 - x / 
$$\frac{2 x^{2}}{\left(9 - x^{2}\right)^{2}} + \frac{1}{9 - x^{2}}$$
The second derivative [src]
    /         2 \
    |      4*x  |
2*x*|3 - -------|
    |          2|
    \    -9 + x /
-----------------
             2   
    /      2\    
    \-9 + x /    
$$\frac{2 x \left(- \frac{4 x^{2}}{x^{2} - 9} + 3\right)}{\left(x^{2} - 9\right)^{2}}$$
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 /              
$$\frac{6 \left(\frac{4 x^{2} \left(\frac{2 x^{2}}{x^{2} - 9} - 1\right)}{x^{2} - 9} - \frac{4 x^{2}}{x^{2} - 9} + 1\right)}{\left(x^{2} - 9\right)^{2}}$$
The graph
Derivative of x/(9-x^2)