Derivative of sqrt(x^5)

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   ____
  /  5 
\/  x

$$\sqrt{x^{5}}$$

sqrt(x^5)

Detail solution

Let $u = x^{5}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{5}$ :
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
The result of the chain rule is:

$\frac{5 x^{4}}{2 \sqrt{x^{5}}}$

The answer is:

$\frac{5 x^{4}}{2 \sqrt{x^{5}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     ____
    /  5 
5*\/  x  
---------
   2*x

$$\frac{5 \sqrt{x^{5}}}{2 x}$$

Simplify

The second derivative [src]

      ____
     /  5 
15*\/  x  
----------
      2   
   4*x

$$\frac{15 \sqrt{x^{5}}}{4 x^{2}}$$

Simplify

The third derivative [src]

      ____
     /  5 
15*\/  x  
----------
      3   
   8*x

$$\frac{15 \sqrt{x^{5}}}{8 x^{3}}$$

Simplify

The graph