1.For any function y+f(x), express dy/dx using limit notation. Give a clear explanation for your given answer.

Question

you probably meant to type y=f(x)

By definition

dy/dx = Limit (f(x+∆x) - f(x))/∆x as ∆x-->0

The explanation of this equation is the whole basis and introduction to Calculus.
It can be found in any introductory Calculus text.