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Derivative of:
Derivative of sin(2*x^2+3)
Derivative of (1+x)/(4-x^2)
Derivative of (1+tan(3*x)^(2))*e^(-x/2)
Derivative of 13*x-13*tan(x)-18
Identical expressions
six *(sqrt(x)^ five)
6 multiply by ( square root of (x) to the power of 5)
six multiply by ( square root of (x) to the power of five)
6*(√(x)^5)
6*(sqrt(x)5)
6*sqrtx5
6*(sqrt(x)⁵)
6(sqrt(x)^5)
6(sqrt(x)5)
6sqrtx5
6sqrtx^5
Similar expressions
6/5^6sqrt(x)^5

The derivative of the function/ 6*(sqrt(x)^5)

Derivative of 6*(sqrt(x)^5)

The solution

You have entered [src]

       5
    ___ 
6*\/ x

$$6 \left(\sqrt{x}\right)^{5}$$

6*(sqrt(x))^5

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $u^{5}$ goes to $5 u^{4}$
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:
  
  $\frac{5 x^{\frac{3}{2}}}{2}$
So, the result is: $15 x^{\frac{3}{2}}$

The answer is:

$15 x^{\frac{3}{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    3/2
15*x

$$15 x^{\frac{3}{2}}$$

Simplify

The second derivative [src]

     ___
45*\/ x 
--------
   2

$$\frac{45 \sqrt{x}}{2}$$

Simplify

The third derivative [src]

   45  
-------
    ___
4*\/ x

$$\frac{45}{4 \sqrt{x}}$$

Simplify