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

Derivative of cbrt(x^3+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
3 /  3     
\/  x  + 1
$$\sqrt[3]{x^{3} + 1}$$ 
(x^3 + 1)^(1/3)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2    
     x     
-----------
        2/3
/ 3    \   
\x  + 1/
$$\frac{x^{2}}{\left(x^{3} + 1\right)^{\frac{2}{3}}}$$
Simplify
The second derivative [src] 
    /       3  \
    |      x   |
2*x*|1 - ------|
    |         3|
    \    1 + x /
----------------
          2/3   
  /     3\      
  \1 + x /
$$\frac{2 x \left(- \frac{x^{3}}{x^{3} + 1} + 1\right)}{\left(x^{3} + 1\right)^{\frac{2}{3}}}$$
Simplify
The third derivative [src] 
  /        3          6  \
  |     6*x        5*x   |
2*|1 - ------ + ---------|
  |         3           2|
  |    1 + x    /     3\ |
  \             \1 + x / /
--------------------------
               2/3        
       /     3\           
       \1 + x /
$$\frac{2 \left(\frac{5 x^{6}}{\left(x^{3} + 1\right)^{2}} - \frac{6 x^{3}}{x^{3} + 1} + 1\right)}{\left(x^{3} + 1\right)^{\frac{2}{3}}}$$
Simplify
The graph
Derivative of cbrt(x^3+1)
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