Can we cancel two differential terms while they are in a ratio. For example if we have (dx/dt) / (dy/dt), can we just directly cancel dt by dt and write it as dx/dy. I mean is is this step allowed?
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Fine, but see https://math.stackexchange.com/questions/942457/understanding-frac-partial-x-partial-y-frac-partial-y-partial-z-frac – Angina Seng Mar 29 '19 at 07:25
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@LordSharktheUnknown for total derivatives (is there a better term?), is this always true? – user1952500 Mar 29 '19 at 07:37
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The "cancellation of differential terms" in $(dx/dt)/(dy/dt)$ can be considered an abuse of notation of the already abusive notation of Leibnitz. – Martín-Blas Pérez Pinilla Mar 29 '19 at 09:55
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Yes The reason for that is quite simple because in differential calculus the Letter "d" denotes a certain amount of change in a quantity So "dx/dy" means "change in x with respect to change in y". By that logic, "dt" in both terms represent change in quantity "t". Being the same "term" they can be cancelled to create a ratio which gives the proportion of change in one quantity with respect to the another.
