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sqrt(x^3-1)
The derivative of the function/ sqrt(x^3-1)

Derivative of sqrt(x^3-1)

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

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The solution

You have entered [src] 
   ________
  /  3     
\/  x  - 1
x3−1\sqrt{x^{3} - 1} 
sqrt(x^3 - 1)
Detail solution

  1. Let u=x3−1u = x^{3} - 1.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(x3−1)\frac{d}{d x} \left(x^{3} - 1\right):

    1. Differentiate x3−1x^{3} - 1 term by term:

      1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

      2. The derivative of the constant −1-1 is zero.

      The result is: 3x23 x^{2}

    The result of the chain rule is:

    3x22x3−1\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}

  4. Now simplify:

    3x22x3−1\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}

The answer is:

3x22x3−1\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}

The graph
02468-8-6-4-2-1010050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        2    
     3*x     
-------------
     ________
    /  3     
2*\/  x  - 1
3x22x3−1\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}
Simplify
The second derivative [src] 
    /           3   \
    |        3*x    |
3*x*|1 - -----------|
    |      /      3\|
    \    4*\-1 + x //
---------------------
        _________    
       /       3     
     \/  -1 + x
3x(−3x34(x3−1)+1)x3−1\frac{3 x \left(- \frac{3 x^{3}}{4 \left(x^{3} - 1\right)} + 1\right)}{\sqrt{x^{3} - 1}}
Simplify
The third derivative [src] 
  /           3             6    \
  |        9*x          27*x     |
3*|1 - ----------- + ------------|
  |      /      3\              2|
  |    2*\-1 + x /     /      3\ |
  \                  8*\-1 + x / /
----------------------------------
              _________           
             /       3            
           \/  -1 + x
3(27x68(x3−1)2−9x32(x3−1)+1)x3−1\frac{3 \left(\frac{27 x^{6}}{8 \left(x^{3} - 1\right)^{2}} - \frac{9 x^{3}}{2 \left(x^{3} - 1\right)} + 1\right)}{\sqrt{x^{3} - 1}}
Simplify
The graph
Derivative of sqrt(x^3-1)
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