Mister Exam

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Derivative of sqrt^3(x)

You have entered [src]

     3
  ___ 
\/ x

$$\left(\sqrt{x}\right)^{3}$$

(sqrt(x))^3

Detail solution

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

$\frac{3 \sqrt{x}}{2}$

The answer is:

$\frac{3 \sqrt{x}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

   3   
-------
    ___
4*\/ x

$$\frac{3}{4 \sqrt{x}}$$

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph