How to differentiate the function f(x)= 3x^3 + 2x^-3 - x^(1/2) + 6?

Firstly the general formula you can use on each of the x terms in the polynomial you are trying to differentiate is; f(x)=xⁿ then f '(x)=nx^n-1 where any constant, c, will differentiate to give 0. This formula basically states that you need to multiply x by it's power and then reduce that power by 1. If there is a coefficient then you still multiply x by it's power but you must remember to also take into account the coefficient e.g. if we have f(x)= 2x² then we multiply 2x by 2 to get 4x and then reduce the power by one to get a final answer of f '(x)=4x¹=4x. Therefore applying this to each of the terms in the given polynomial we get an answer of f '(x)= 9x² - 6x^-4 - (1/2)x^-1/2