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

Derivative of cbrt(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
3 _______
\/ x + 1
$$\sqrt[3]{x + 1}$$ 
(x + 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] 
     1      
------------
         2/3
3*(x + 1)
$$\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}}}$$
Simplify
The second derivative [src] 
    -2      
------------
         5/3
9*(1 + x)
$$- \frac{2}{9 \left(x + 1\right)^{\frac{5}{3}}}$$
Simplify
The third derivative [src] 
      10     
-------------
          8/3
27*(1 + x)
$$\frac{10}{27 \left(x + 1\right)^{\frac{8}{3}}}$$
Simplify
The graph
Derivative of cbrt(x+1)
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