Cancelling differential terms 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?
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.
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.