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Integral of d{x}:
1/(x^3+1)^2
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Similar expressions
1/(x^3-1)^2

The derivative of the function/ 1/(x^3+1)^2

Derivative of 1/(x^3+1)^2

The solution

You have entered [src]

    1    
---------
        2
/ 3    \ 
\x  + 1/

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

1/((x^3 + 1)^2)

Detail solution

Let $u = \left(x^{3} + 1\right)^{2}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{3} + 1\right)^{2}$ :
1. Let $u = x^{3} + 1$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{3} + 1\right)$ :
  1. Differentiate $x^{3} + 1$ term by term:
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    2. The derivative of the constant $1$ is zero.
    The result is: $3 x^{2}$
  The result of the chain rule is:
  
  $3 x^{2} \left(2 x^{3} + 2\right)$
The result of the chain rule is:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    /         3 \
    |      9*x  |
6*x*|-2 + ------|
    |          3|
    \     1 + x /
-----------------
            3    
    /     3\     
    \1 + x /

$$\frac{6 x \left(\frac{9 x^{3}}{x^{3} + 1} - 2\right)}{\left(x^{3} + 1\right)^{3}}$$

Simplify

The third derivative [src]

   /           6         3 \
   |       54*x      27*x  |
12*|-1 - --------- + ------|
   |             2        3|
   |     /     3\    1 + x |
   \     \1 + x /          /
----------------------------
                 3          
         /     3\           
         \1 + x /

$$\frac{12 \left(- \frac{54 x^{6}}{\left(x^{3} + 1\right)^{2}} + \frac{27 x^{3}}{x^{3} + 1} - 1\right)}{\left(x^{3} + 1\right)^{3}}$$

Simplify

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Derivative of 1/(x^3+1)^2

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The solution