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Derivative of:
Derivative of (x-7)^2
Derivative of (x+1)/(x^2+1)
Derivative of (x^2)^(1/3)
Derivative of sqrt(x/2)
Integral of d{x}:
(x^2)^(1/3)
Graphing y =:
(x^2)^(1/3)
Limit of the function:
(x^2)^(1/3)
Identical expressions
(x^ two)^(one / three)
(x squared ) to the power of (1 divide by 3)
(x to the power of two) to the power of (one divide by three)
(x2)(1/3)
x21/3
(x²)^(1/3)
(x to the power of 2) to the power of (1/3)
x^2^1/3
(x^2)^(1 divide by 3)
Similar expressions
4*(x^2^(1/3))

The derivative of the function/ (x^2)^(1/3)

Derivative of (x^2)^(1/3)

The solution

You have entered [src]

   ____
3 /  2 
\/  x

$$\sqrt[3]{x^{2}}$$

(x^2)^(1/3)

Detail solution

Let $u = x^{2}$ .
Apply the power rule: $\sqrt[3]{u}$ goes to $\frac{1}{3 u^{\frac{2}{3}}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
The result of the chain rule is:

$\frac{2 x}{3 \left|{x}\right|^{\frac{4}{3}}}$
Now simplify:

$\frac{2 x}{3 \left|{x^{\frac{4}{3}}}\right|}$

The answer is:

$\frac{2 x}{3 \left|{x^{\frac{4}{3}}}\right|}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2/3
2*|x|   
--------
  3*x

$$\frac{2 \left|{x}\right|^{\frac{2}{3}}}{3 x}$$

Simplify

The second derivative [src]

  /       2/3            \
  |  3*|x|      2*sign(x)|
2*|- -------- + ---------|
  |     x        3 _____ |
  \              \/ |x|  /
--------------------------
           9*x

$$\frac{2 \left(\frac{2 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} - \frac{3 \left|{x}\right|^{\frac{2}{3}}}{x}\right)}{9 x}$$

Simplify

The third derivative [src]

  /      2                             2/3            \
  |  sign (x)   6*DiracDelta(x)   9*|x|      6*sign(x)|
4*|- -------- + --------------- + -------- - ---------|
  |      4/3        3 _____           2        3 _____|
  \   |x|           \/ |x|           x       x*\/ |x| /
-------------------------------------------------------
                          27*x

$$\frac{4 \left(\frac{6 \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} - \frac{6 \operatorname{sign}{\left(x \right)}}{x \sqrt[3]{\left|{x}\right|}} + \frac{9 \left|{x}\right|^{\frac{2}{3}}}{x^{2}}\right)}{27 x}$$

Simplify

The graph

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Identical expressions

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Derivative of (x^2)^(1/3)

The graph:

Piecewise:

The solution