Mister Exam

Derivative of sqrt(2*x)-3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  _____    
\/ 2*x  - 3
$$\sqrt{2 x} - 3$$
sqrt(2*x) - 3
Detail solution
  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:


The answer is:

The graph
The first derivative [src]
  ___   ___
\/ 2 *\/ x 
-----------
    2*x    
$$\frac{\sqrt{2} \sqrt{x}}{2 x}$$
The second derivative [src]
   ___ 
-\/ 2  
-------
    3/2
 4*x   
$$- \frac{\sqrt{2}}{4 x^{\frac{3}{2}}}$$
The third derivative [src]
    ___
3*\/ 2 
-------
    5/2
 8*x   
$$\frac{3 \sqrt{2}}{8 x^{\frac{5}{2}}}$$
The graph
Derivative of sqrt(2*x)-3