I am searching for a book on Calculus which explains in detail and with diagrams how the equation/formula/method was derived. All books I've read in the past merely explain a systematic approach towards solving a mathematical problem, but I have not learned how it works; a simple example, what is sine and how does one go about re-discovering sine?
Does such a book exist? I don't want a book on the history of mathematics, I would like a book which teaches it to me and explains how and why it works.
I want to UNDERSTAND mathematics, not just do it!