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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
(x)3\left(\sqrt{x}\right)^{3} 
(sqrt(x))^3
Detail solution

  1. Let u=xu = \sqrt{x}.

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

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

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

    The result of the chain rule is:

    3x2\frac{3 \sqrt{x}}{2}

The answer is:

3x2\frac{3 \sqrt{x}}{2}

The graph
02468-8-6-4-2-1010050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3/2
3*x   
------
 2*x
3x322x\frac{3 x^{\frac{3}{2}}}{2 x}
Simplify
The second derivative [src] 
   3   
-------
    ___
4*\/ x
34x\frac{3}{4 \sqrt{x}}
Simplify
The third derivative [src] 
 -3   
------
   3/2
8*x
−38x32- \frac{3}{8 x^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt^3(x)
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