Question

What is a Derivative

Answer 1

Have you tried wikipedia? A lot of the math articles are dense but the derivative entry is in pretty decipherable english: http://en.wikipedia.org/wiki/Derivative

A derivative is essentially a rate of change. When you calculate the derivative of a function at a certain point, you are looking for the rate that y changes in relation to x. In other words, you're asking "when I change one variable in this equation, how much does the other variable change as a result? "

Answer 2

Think of the derivative in terms of: for every action there is an equal and opposite reaction.
Maybe you are a pool player? ;)

Answer 3

Check out this course:
MIT 18.01 David Jerison