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This notation reminds people that the derivative is the limit of ratios of change and/ or a limit of fractions. Newton's work included: linking infinite sums and the algebraic expressions of the inverse relation between tangents and areas. Previous to their discovery, rectangles were used to find area, though the estimated area was always too little or too much; calculus allowed these rectangles to be "infinitely thin"("Integration")...
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Previous to their discovery, rectangles were used to find area, though the estimated area was always too little or too much; calculus allowed these rectangles to be "infinitely thin"("Integration"). Algebra is not useful to find areas under a curve, unlike calculus, which allows people to work with "continuously vary quantities" of figures ("Calculus: Math in flux")...
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