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Derivative of:
Derivative of 1/3*x^3
Derivative of x*x^(1/2)
Derivative of x^(5/2)
Derivative of (x-4)^2
Integral of d{x}:
x*x^(1/2)
Identical expressions
x*x^(one / two)
x multiply by x to the power of (1 divide by 2)
x multiply by x to the power of (one divide by two)
x*x(1/2)
x*x1/2
xx^(1/2)
xx(1/2)
xx1/2
xx^1/2
x*x^(1 divide by 2)
Similar expressions
y=x^(2)*(1-x*x^((1)/(2)))

The derivative of the function/ x*x^(1/2)

Derivative of x*x^(1/2)

The solution

You have entered [src]

    ___
x*\/ x

$$\sqrt{x} x$$

d /    ___\
--\x*\/ x /
dx

$$\frac{d}{d x} \sqrt{x} x$$

Transform

Detail solution

Apply the product rule:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    ___
3*\/ x 
-------
   2

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

Simplify

The second derivative [src]

   3   
-------
    ___
4*\/ x

$$\frac{3}{4 \sqrt{x}}$$

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of x*x^(1/2)