How to differentiate expressions in x involving negative & fractional exponents (by example)

The rule for differentiating powers of x apply to negative, fractional and irrational powers of x.

Multiply the term by the power, then reduce the power by 1.

In this example, the derivative of the function f(x) = 2x^(-4) + x^(2/3) is

f'(x) = -8x^(-5) + (2/3)x^(-1/3)