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So I was wondering if manipulating differential as fraction is fine.In Physics problems ,usually, what I see is if we have equations of magnetic field ,we consider a magnetic field caused by a small length dl and the magnetic field is dB and integrating over the whole length.it seems we are treating dB as a infintesimal quantity.However ,after browsing for a while,the answer is that the notation dy/dx is not a infintesimal quantity but rather an operation on the function y.I am confused as to how it is valid in physics to treat it as infintesimal quantities.(After learning it,my notion for physics just got crushed and am now confused).I have not learned multivariable calculus yet,but from the arguments I've read ,I found that interpreting them as fractions does not work anymore.But it seems it works fine when in 2 dimensions.In mechanics when we derive equation for rocket motion (ejecting mass) we interpret differential as small quantities (dm) and divide by small time dt.Sorry for the long story... I am confused right now

TL:DR : In physics ,dy/dx can be operated as if it was a small quantity divided by small quantity,though from what I've read it is not supposed to be a ratio.

When does interpreting them work and when does it not. Any help would be very much appreciated ...

Winston Cahya
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I think you meant "derivatives" rather than "differentials" and are asking if it is valid to "treat derivatives as fractions with differentials as numerator and denominator".

Yes, it is. To show that any given property of a fraction still holds for a derivative, go back before the limit in the definition of the derivative to the "difference quotient", use the fraction property, then take the limit.

user247327
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