Mister Exam

Other calculators


(sqrt(2*x)-3)/6

Derivative of (sqrt(2*x)-3)/6

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  _____    
\/ 2*x  - 3
-----------
     6     
$$\frac{\sqrt{2 x} - 3}{6}$$
  /  _____    \
d |\/ 2*x  - 3|
--|-----------|
dx\     6     /
$$\frac{d}{d x} \frac{\sqrt{2 x} - 3}{6}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Differentiate term by term:

      1. Let .

      2. Apply the power rule: goes to

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

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result of the chain rule is:

      4. The derivative of the constant is zero.

      The result is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
   ___  
 \/ 2   
--------
     ___
12*\/ x 
$$\frac{\sqrt{2}}{12 \sqrt{x}}$$
The second derivative [src]
   ___ 
-\/ 2  
-------
    3/2
24*x   
$$- \frac{\sqrt{2}}{24 x^{\frac{3}{2}}}$$
The third derivative [src]
   ___ 
 \/ 2  
-------
    5/2
16*x   
$$\frac{\sqrt{2}}{16 x^{\frac{5}{2}}}$$
The graph
Derivative of (sqrt(2*x)-3)/6