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(x^3)/(4-x^2)

Derivative of (x^3)/(4-x^2)

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

The graph:

from to

Piecewise:

The solution

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