Mister Exam

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Derivative of x^(-2/3)

You have entered [src]

 1  
----
 2/3
x

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

x^(-2/3)

Detail solution

Apply the power rule: $\frac{1}{x^{\frac{2}{3}}}$ goes to $- \frac{2}{3 x^{\frac{5}{3}}}$

The answer is:

$- \frac{2}{3 x^{\frac{5}{3}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 -2   
------
   5/3
3*x

$$- \frac{2}{3 x^{\frac{5}{3}}}$$

Simplify

The second derivative [src]

  10  
------
   8/3
9*x

$$\frac{10}{9 x^{\frac{8}{3}}}$$

Simplify

The third derivative [src]

  -80   
--------
    11/3
27*x

$$- \frac{80}{27 x^{\frac{11}{3}}}$$

Simplify

The graph