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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

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The solution

You have entered [src] 
3 _______
\/ x + 1
x+13\sqrt[3]{x + 1} 
(x + 1)^(1/3)
Detail solution

  1. Let u=x+1u = x + 1.

  2. Apply the power rule: u3\sqrt[3]{u} goes to 13u23\frac{1}{3 u^{\frac{2}{3}}}

  3. Then, apply the chain rule. Multiply by ddx(x+1)\frac{d}{d x} \left(x + 1\right):

    1. Differentiate x+1x + 1 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 11 is zero.

      The result is: 11

    The result of the chain rule is:

    13(x+1)23\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}}}

  4. Now simplify:

    13(x+1)23\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}}}

The answer is:

13(x+1)23\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}}}

The graph
02468-8-6-4-2-10100.02.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1      
------------
         2/3
3*(x + 1)
13(x+1)23\frac{1}{3 \left(x + 1\right)^{\frac{2}{3}}}
Simplify
The second derivative [src] 
    -2      
------------
         5/3
9*(1 + x)
−29(x+1)53- \frac{2}{9 \left(x + 1\right)^{\frac{5}{3}}}
Simplify
The third derivative [src] 
      10     
-------------
          8/3
27*(1 + x)
1027(x+1)83\frac{10}{27 \left(x + 1\right)^{\frac{8}{3}}}
Simplify
The graph
Derivative of cbrt(x+1)
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