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