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Because calculus is the first class where functions (e.g. derive, indefinite intergration) take a function as its input, and outputs a function.


No, all functions do that. Consider the functions f(x)=x^2, and g(x). f(2)=4, but f(g(x))=g(x)^2. A more intuitive example would be abs(x)=|x|. For any numeric input, you get a numeric output, but for a functional input, g(x), you get g`(x) as an output, where g`(x) is a new function simmilar to, but possibly different from, g(x).




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