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Derivative of:
Derivative of x*sqrt(3-x)
Derivative of x^6/6
Derivative of x^3-3*x
Derivative of x^2+4x
Identical expressions
one /3sqrt(x^ five)
1 divide by 3 square root of (x to the power of 5)
one divide by 3 square root of (x to the power of five)
1/3√(x^5)
1/3sqrt(x5)
1/3sqrtx5
1/3sqrt(x⁵)
1/3sqrtx^5
1 divide by 3sqrt(x^5)

The derivative of the function/ 1/3sqrt(x^5)

Derivative of 1/3sqrt(x^5)

The solution

You have entered [src]

   ____
  /  5 
\/  x  
-------
   3

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

sqrt(x^5)/3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{5}$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. 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:
  
  $\frac{5 x^{4}}{2 \sqrt{x^{5}}}$
So, the result is: $\frac{5 x^{4}}{6 \sqrt{x^{5}}}$

The answer is:

$\frac{5 x^{4}}{6 \sqrt{x^{5}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     ____
    /  5 
5*\/  x  
---------
   6*x

$$\frac{5 \sqrt{x^{5}}}{6 x}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify