Calculus was developed by Newton and Leibnitz independently in the late 17th century, and it was put on a rigorous basis by Riemann and others in the mid 19th century. That is: mathematicians have been writing about calculus for a very, very long time, and the odds are that somebody in that span of time has written a clearer and better explanation of it than people writing about it today. (New is not necessarily better.)
That I said, I would give a loud shout out to Howard Anton's _Calculus with Analytic Geometry_. Very well written, covers the ground more thoroughly than any other text I've seen. Forty years on, it's right above my desk for reference.