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Derivative of:
Derivative of x^-3
Derivative of x^2*sqrt(x)
Derivative of 1/2*x^2
Derivative of x*(log(x)/log(10))
Graphing y =:
x^2*sqrt(x)
Integral of d{x}:
x^2*sqrt(x)
Canonical form:
x^2*sqrt(x)
Identical expressions
x^ two *sqrt(x)
x squared multiply by square root of (x)
x to the power of two multiply by square root of (x)
x^2*√(x)
x2*sqrt(x)
x2*sqrtx
x²*sqrt(x)
x to the power of 2*sqrt(x)
x^2sqrt(x)
x2sqrt(x)
x2sqrtx
x^2sqrtx
Similar expressions
y=e^(-4*x^2)*sqrt(x-4*x^2)

The derivative of the function/ x^2*sqrt(x)

Derivative of x^2*sqrt(x)

The solution

You have entered [src]

 2   ___
x *\/ x

$$\sqrt{x} x^{2}$$

x^2*sqrt(x)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = \sqrt{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
The result is: $\frac{5 x^{\frac{3}{2}}}{2}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3/2
5*x   
------
  2

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

Simplify

The second derivative [src]

     ___
15*\/ x 
--------
   4

$$\frac{15 \sqrt{x}}{4}$$

Simplify

The third derivative [src]

   15  
-------
    ___
8*\/ x

$$\frac{15}{8 \sqrt{x}}$$

Simplify

The graph

Derivative of x^2*sqrt(x)