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As $$\frac{dy}{dx}= \lim_{∆x \to 0}\frac{∆y}{∆x}$$ then why $$\frac{dy}{dx}$$ is not a ratio ?

user677491
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  • It is a number, because the "limit of the ratio..." is defined to be a real number. – Mauro ALLEGRANZA Jul 05 '19 at 15:03
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    A ratio of what to what? – Asura Path Jul 05 '19 at 15:25
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    What do you mean by a ratio? Every number is a ratio with denominator one. – copper.hat Jul 05 '19 at 15:49
  • I think you can think of it as a ratio. It is the "rate of change" in y with respect to change in x. Also if you have dy/dx=x, for instance, you could write it as dy=x.dx, integrating both sides, you get: y+c1=x2/2 + c2. You could also consider it as symbol as in the answer. – NoChance Jul 05 '19 at 16:07

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$\frac{dy}{dx}$ is simply (Leibnitz) notation for the derivative. It is a symbol, like $y'$, $y'(x)$, and so forth.

DDS
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