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sqrt(4x)
The derivative of the function/ sqrt(4x)

Derivative of sqrt(4x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _____
\/ 4*x
4x\sqrt{4 x} 
d /  _____\
--\\/ 4*x /
dx
ddx4x\frac{d}{d x} \sqrt{4 x}
Transform
Detail solution

  1. Let u=4xu = 4 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 ddx4x\frac{d}{d x} 4 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: 44

    The result of the chain rule is:

    1x\frac{1}{\sqrt{x}}

The answer is:

1x\frac{1}{\sqrt{x}}

The graph
02468-8-6-4-2-1010010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    ___
2*\/ x 
-------
  2*x
2x2x\frac{2 \sqrt{x}}{2 x}
Simplify
The second derivative [src] 
 -1   
------
   3/2
2*x
−12x32- \frac{1}{2 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
  3   
------
   5/2
4*x
34x52\frac{3}{4 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(4x)
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