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

Derivative of x*sqrt(x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    g(x)=xg{\left(x \right)} = \sqrt{x}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

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

    The result 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*\/ x 
-------
   2
3x2\frac{3 \sqrt{x}}{2}
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 x*sqrt(x)
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