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Derivative of:
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Derivative of tan(x/2)-cot(x/2)
Derivative of sqrt(x^3-1)
Derivative of sin(x)*cos(x)+x
Graphing y =:
sqrt(x^3-1)
Identical expressions
sqrt(x^ three - one)
square root of (x cubed minus 1)
square root of (x to the power of three minus one)
√(x^3-1)
sqrt(x3-1)
sqrtx3-1
sqrt(x³-1)
sqrt(x to the power of 3-1)
sqrtx^3-1
Similar expressions
sqrt(x^3+1)

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

Derivative of sqrt(x^3-1)

The solution

You have entered [src]

   ________
  /  3     
\/  x  - 1

$$\sqrt{x^{3} - 1}$$

sqrt(x^3 - 1)

Detail solution

Let $u = x^{3} - 1$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
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:

$\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}$
Now simplify:

$\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}$

The answer is:

$\frac{3 x^{2}}{2 \sqrt{x^{3} - 1}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2    
     3*x     
-------------
     ________
    /  3     
2*\/  x  - 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

$$\frac{3 x \left(- \frac{3 x^{3}}{4 \left(x^{3} - 1\right)} + 1\right)}{\sqrt{x^{3} - 1}}$$

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

$$\frac{3 \left(\frac{27 x^{6}}{8 \left(x^{3} - 1\right)^{2}} - \frac{9 x^{3}}{2 \left(x^{3} - 1\right)} + 1\right)}{\sqrt{x^{3} - 1}}$$

Simplify

The graph

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Derivative of sqrt(x^3-1)

The graph:

Piecewise:

The solution