Issac Newton and Leibniz developed it independently.
Newton discovered it first, but kept it to himself. Leibniz, on the other hand, published. Newton accused Liebnitz of stealing his ideas, thus starting a long feud between the two.
Today, they are both recognized as being the founding fathers of calculus. It is however, Leibniz's notation of the calculus that has flourished.
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Calculus; by a long shot.
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.
It is certainly used in calculus, just as calculus can be used in trigonometry.
No. Calculus if a field of mathematics.
Calculus is the correct spelling.