Mister Exam

Other calculators

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

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
       5
    ___ 
6*\/ x  
$$6 \left(\sqrt{x}\right)^{5}$$
6*(sqrt(x))^5
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
    3/2
15*x   
$$15 x^{\frac{3}{2}}$$
The second derivative [src]
     ___
45*\/ x 
--------
   2    
$$\frac{45 \sqrt{x}}{2}$$
The third derivative [src]
   45  
-------
    ___
4*\/ x 
$$\frac{45}{4 \sqrt{x}}$$