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Derivative of:
Derivative of sin(x)/cos(x)
Derivative of cos(x)^(3)
Derivative of 1/(2*sqrt(x))
Derivative of x^5*sin(x)
Identical expressions
six /(x^(two / three))
6 divide by (x to the power of (2 divide by 3))
six divide by (x to the power of (two divide by three))
6/(x(2/3))
6/x2/3
6/x^2/3
6 divide by (x^(2 divide by 3))

The derivative of the function/ 6/(x^(2/3))

Derivative of 6/(x^(2/3))

The solution

You have entered [src]

 6  
----
 2/3
x

\frac{6}{x^{\frac{2}{3}}}

d / 6  \
--|----|
dx| 2/3|
  \x   /

\frac{d}{d x} \frac{6}{x^{\frac{2}{3}}}

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{\frac{2}{3}}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{\frac{2}{3}}$ :
  1. Apply the power rule: $x^{\frac{2}{3}}$ goes to $\frac{2}{3 \sqrt[3]{x}}$
  The result of the chain rule is:
  
  $- \frac{2}{3 x^{\frac{5}{3}}}$
So, the result is: $- \frac{4}{x^{\frac{5}{3}}}$

The answer is:

- \frac{4}{x^{\frac{5}{3}}}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4  
----
 5/3
x

- \frac{4}{x^{\frac{5}{3}}}

Simplify

The second derivative [src]

  20  
------
   8/3
3*x

\frac{20}{3 x^{\frac{8}{3}}}

Simplify

The third derivative [src]

 -160  
-------
   11/3
9*x

- \frac{160}{9 x^{\frac{11}{3}}}

Simplify

The graph

Derivative of 6/(x^(2/3))