Rewrite the function with exponents.

`f(x) = x^(1/2)-6x^(1/3)`

Use the power rule to solve.

`f'(x) = 1/2 x^(-1/2)-(1/3)6x^(-2/3)`

Simplify and eliminate the negative fractions by writing them as a fraction.

`f'(x) = 1/(2x^(1/2))-2/x^(2/3)`

Rewrite the function with exponents.

`f(x) = x^(1/2)-6x^(1/3)`

Use the power rule to solve.

`f'(x) = 1/2 x^(-1/2)-(1/3)6x^(-2/3)`

Simplify and eliminate the negative fractions by writing them as a fraction.

`f'(x) = 1/(2x^(1/2))-2/x^(2/3)`