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y=(x)^2sqrt(x)

Derivative of y=(x)^2sqrt(x)

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src]
 2   ___
x *\/ x 
xx2\sqrt{x} x^{2}
d / 2   ___\
--\x *\/ x /
dx          
ddxxx2\frac{d}{d x} \sqrt{x} x^{2}
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)=x2f{\left(x \right)} = x^{2}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x2x^{2} goes to 2x2 x

    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: 5x322\frac{5 x^{\frac{3}{2}}}{2}


The answer is:

5x322\frac{5 x^{\frac{3}{2}}}{2}

The graph
02468-8-6-4-2-10100500
The first derivative [src]
   3/2
5*x   
------
  2   
5x322\frac{5 x^{\frac{3}{2}}}{2}
The second derivative [src]
     ___
15*\/ x 
--------
   4    
15x4\frac{15 \sqrt{x}}{4}
The third derivative [src]
   15  
-------
    ___
8*\/ x 
158x\frac{15}{8 \sqrt{x}}
The graph
Derivative of y=(x)^2sqrt(x)