Derivative of sqrt(x)^(4)

You have entered [src]

     4
  ___ 
\/ x

$$\left(\sqrt{x}\right)^{4}$$

(sqrt(x))^4

Detail solution

Let $u = \sqrt{x}$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
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:

$2 x$

The answer is:

$2 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2
2*x 
----
 x

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

Simplify

The second derivative [src]

$$2$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph