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sqrt(2x)
The derivative of the function/ sqrt(2x)

Derivative of sqrt(2x)

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

The graph:

from to

Piecewise:

The solution

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

  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:

The answer is:

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