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1/(x^3+1)

Derivative of 1/(x^3+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    1   
1*------
   3    
  x  + 1
$$1 \cdot \frac{1}{x^{3} + 1}$$
d /    1   \
--|1*------|
dx|   3    |
  \  x  + 1/
$$\frac{d}{d x} 1 \cdot \frac{1}{x^{3} + 1}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of the constant is zero.

    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:


The answer is:

The graph
The first derivative [src]
      2  
  -3*x   
---------
        2
/ 3    \ 
\x  + 1/ 
$$- \frac{3 x^{2}}{\left(x^{3} + 1\right)^{2}}$$
The second derivative [src]
    /         3 \
    |      3*x  |
6*x*|-1 + ------|
    |          3|
    \     1 + x /
-----------------
            2    
    /     3\     
    \1 + x /     
$$\frac{6 x \left(\frac{3 x^{3}}{x^{3} + 1} - 1\right)}{\left(x^{3} + 1\right)^{2}}$$
The third derivative [src]
   /        3          6  \
   |    18*x       27*x   |
-6*|1 - ------ + ---------|
   |         3           2|
   |    1 + x    /     3\ |
   \             \1 + x / /
---------------------------
                 2         
         /     3\          
         \1 + x /          
$$- \frac{6 \cdot \left(\frac{27 x^{6}}{\left(x^{3} + 1\right)^{2}} - \frac{18 x^{3}}{x^{3} + 1} + 1\right)}{\left(x^{3} + 1\right)^{2}}$$
The graph
Derivative of 1/(x^3+1)