Given that y = 4x^3 -1 + 2x^1/2 (where x>0) find dy/dx.

This is an example of a common AS differentiation Q. To find dy/dx simply apply the power rule to each term in the equation. The power rule is if you have a term x^n then dy/dx will be n times x^(n-1). e.g. for 4x^3 we multiply 3 by 4 for our coefficient and subtract 1 from the power giving us 12x^2. So here dy/dx = 12x^2 + x^-1/2.