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sqrt(3*x)
The derivative of the function/ sqrt(3*x)

Derivative of sqrt(3*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _____
\/ 3*x
3x\sqrt{3 x} 
d /  _____\
--\\/ 3*x /
dx
ddx3x\frac{d}{d x} \sqrt{3 x}
Transform
Detail solution

  1. Let u=3xu = 3 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 ddx3x\frac{d}{d x} 3 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: 33

    The result of the chain rule is:

    32x\frac{\sqrt{3}}{2 \sqrt{x}}

The answer is:

32x\frac{\sqrt{3}}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  ___   ___
\/ 3 *\/ x 
-----------
    2*x
3x2x\frac{\sqrt{3} \sqrt{x}}{2 x}
Simplify
The second derivative [src] 
   ___ 
-\/ 3  
-------
    3/2
 4*x
−34x32- \frac{\sqrt{3}}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
    ___
3*\/ 3 
-------
    5/2
 8*x
338x52\frac{3 \sqrt{3}}{8 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(3*x)
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