Derivative of sqrt^8(x)

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     8
  ___ 
\/ x

$$\left(\sqrt{x}\right)^{8}$$

(sqrt(x))^8

Detail solution

Let $u = \sqrt{x}$ .
Apply the power rule: $u^{8}$ goes to $8 u^{7}$
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:

$4 x^{3}$

The answer is:

$4 x^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4
4*x 
----
 x

$$\frac{4 x^{4}}{x}$$

Simplify

The second derivative [src]

    2
12*x

$$12 x^{2}$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify