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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
$$\sqrt{4 x}$$ 
d /  _____\
--\\/ 4*x /
dx
$$\frac{d}{d x} \sqrt{4 x}$$
Transform
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
$$\frac{2 \sqrt{x}}{2 x}$$
Simplify
The second derivative [src] 
 -1   
------
   3/2
2*x
$$- \frac{1}{2 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  3   
------
   5/2
4*x
$$\frac{3}{4 x^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(4x)
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