Mister Exam

Other calculators


x^3/(x-1)

Derivative of x^3/(x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3 
  x  
-----
x - 1
$$\frac{x^{3}}{x - 1}$$
x^3/(x - 1)
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:

  2. Now simplify:


The answer is:

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