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Derivative of:
Derivative of x^6/6
Derivative of x^(5/2)
Derivative of x^3/x
Derivative of x^3*sqrt(x)
Integral of d{x}:
x^3*sqrt(x)
Identical expressions
x^ three *sqrt(x)
x cubed multiply by square root of (x)
x to the power of three multiply by square root of (x)
x^3*√(x)
x3*sqrt(x)
x3*sqrtx
x³*sqrt(x)
x to the power of 3*sqrt(x)
x^3sqrt(x)
x3sqrt(x)
x3sqrtx
x^3sqrtx

The derivative of the function/ x^3*sqrt(x)

Derivative of x^3*sqrt(x)

The solution

You have entered [src]

 3   ___
x *\/ x

$$\sqrt{x} x^{3}$$

x^3*sqrt(x)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
$g{\left(x \right)} = \sqrt{x}$ ; 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: $\frac{7 x^{\frac{5}{2}}}{2}$

The answer is:

$\frac{7 x^{\frac{5}{2}}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   5/2
7*x   
------
  2

$$\frac{7 x^{\frac{5}{2}}}{2}$$

Simplify

The second derivative [src]

    3/2
35*x   
-------
   4

$$\frac{35 x^{\frac{3}{2}}}{4}$$

Simplify

The third derivative [src]

      ___
105*\/ x 
---------
    8

$$\frac{105 \sqrt{x}}{8}$$

Simplify

The graph

Derivative of x^3*sqrt(x)