it was invented by a greek alphabetition to keep track of his letters using simple maths, unfortunately he found when he made many letters, he lost track of how many he had, so he would write 2a+3b=13 as a simple method of remembering
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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.
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
It is certainly used in calculus, just as calculus can be used in trigonometry.
No. Calculus if a field of mathematics.