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Derivative of:
Derivative of -3/x
Derivative of x*x
Derivative of x^(2*x)
Derivative of x*cot(x)
Identical expressions
(а/x^(two / three))
(а divide by x to the power of (2 divide by 3))
(а divide by x to the power of (two divide by three))
(а/x(2/3))
а/x2/3
а/x^2/3
(а divide by x^(2 divide by 3))

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

Derivative of (а/x^(2/3))

The solution

You have entered [src]

 a  
----
 2/3
x

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

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

$$\frac{\partial}{\partial x} \frac{a}{x^{\frac{2}{3}}}$$

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

The answer is:

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

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify