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Abuse of Notations?

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Hey guys, umm i'm just gonna get straight to the point, why is the notation of dy/dx for example is being abused so badly? it's not a fraction right? because you can express it in newtonian notation like y' too! i mean it's just a notation to represent the change in y respect to x
I was learning about the capstan equation for example and derivation abused it like this:
http://en.wikipedia.org/wiki/Capstan_equation
look at (7), how could you express d/dx= ????
can someone explain this to me? please

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