That is the part of calculus that is basically concerned about calculating derivatives. A derivative can be understood as the slope of a curve. For example, the line y = 2x has a slope of 2 at any point of the line, while the parabola y = x squared has a slope of 2x at any point of the curve.
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Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
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xx + sincos
http://en.wikipedia.org/wiki/History_of_calculus Have a look at this wikipedia article. It has a great history of calculus.
Calc 2, then Calc 3, then usually Differential Equations