How do you find the derivative of a function using the power rule, and can you provide an example?

The power rule states that if you have a function of the form $f(x) = x^n$, the derivative is:

$$ f'(x) = n \cdot x^{n-1} $$

For example, if $f(x) = x^3$, then:

$$ f'(x) = 3 \cdot x^2 $$