I am trying to teach myself calculus using online videos and other webpages, and I'm now having trouble making sense of the difference quotient. I have a good grasp of the underlying idea of derivatives, and sort of understand how the difference quotient works. I could probably solve any relatively easy problem, simply by plugging in the necessary numbers into the formula of the difference quotient. However, I really don't know what all the components of the formula actually mean. Could somebody break down each part of the formula and explain why it is written the way it is.