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

Derivative of sqrt(2*x)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

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

  1. Let u=2xu = 2 x.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx2x\frac{d}{d x} 2 x:

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

      1. Apply the power rule: xx goes to 11

      So, the result is: 22

    The result of the chain rule is:

    22x\frac{\sqrt{2}}{2 \sqrt{x}}

The answer is:

22x\frac{\sqrt{2}}{2 \sqrt{x}}

The graph
02468-8-6-4-2-101005
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  ___   ___
\/ 2 *\/ x 
-----------
    2*x
2x2x\frac{\sqrt{2} \sqrt{x}}{2 x}
Simplify
The second derivative [src] 
   ___ 
-\/ 2  
-------
    3/2
 4*x
−24x32- \frac{\sqrt{2}}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
    ___
3*\/ 2 
-------
    5/2
 8*x
328x52\frac{3 \sqrt{2}}{8 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(2*x)
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