Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^2*sqrt(1-x^2)
Derivative of e^x*x^2
Derivative of (x+3)/(x-3)
Derivative of x^3/(x^2-4)
Integral of d{x}:
x^3/(x^2-4)
Graphing y =:
x^3/(x^2-4)
How do you in partial fractions?:
x^3/(x^2-4)
Identical expressions
x^ three /(x^ two - four)
x cubed divide by (x squared minus 4)
x to the power of three divide by (x to the power of two minus four)
x3/(x2-4)
x3/x2-4
x³/(x²-4)
x to the power of 3/(x to the power of 2-4)
x^3/x^2-4
x^3 divide by (x^2-4)
Similar expressions
x^3/(x^2+4)

The derivative of the function/ x^3/(x^2-4)

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

The solution

You have entered [src]

   3  
  x   
------
 2    
x  - 4

$$\frac{x^{3}}{x^{2} - 4}$$

x^3/(x^2 - 4)

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{3}$ and $g{\left(x \right)} = x^{2} - 4$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} - 4$ term by term:
  1. The derivative of the constant $-4$ 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:

$\frac{- 2 x^{4} + 3 x^{2} \left(x^{2} - 4\right)}{\left(x^{2} - 4\right)^{2}}$
Now simplify:

$\frac{x^{2} \left(x^{2} - 12\right)}{\left(x^{2} - 4\right)^{2}}$

The answer is:

$\frac{x^{2} \left(x^{2} - 12\right)}{\left(x^{2} - 4\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        4         2 
     2*x       3*x  
- --------- + ------
          2    2    
  / 2    \    x  - 4
  \x  - 4/

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

Simplify

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

$$\frac{2 x \left(\frac{x^{2} \left(\frac{4 x^{2}}{x^{2} - 4} - 1\right)}{x^{2} - 4} - \frac{6 x^{2}}{x^{2} - 4} + 3\right)}{x^{2} - 4}$$

Simplify

The third derivative [src]

  /                   /          2 \        /          2 \\
  |                 4 |       2*x  |      2 |       4*x  ||
  |              4*x *|-1 + -------|   3*x *|-1 + -------||
  |         2         |           2|        |           2||
  |      6*x          \     -4 + x /        \     -4 + x /|
6*|1 - ------- - ------------------- + -------------------|
  |          2                 2                   2      |
  |    -4 + x         /      2\              -4 + x       |
  \                   \-4 + x /                           /
-----------------------------------------------------------
                                2                          
                          -4 + x

$$\frac{6 \left(- \frac{4 x^{4} \left(\frac{2 x^{2}}{x^{2} - 4} - 1\right)}{\left(x^{2} - 4\right)^{2}} + \frac{3 x^{2} \left(\frac{4 x^{2}}{x^{2} - 4} - 1\right)}{x^{2} - 4} - \frac{6 x^{2}}{x^{2} - 4} + 1\right)}{x^{2} - 4}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The graph:

Piecewise:

The solution