4 ms·
Yes, it is possible to treat d as a differential operator, and then dy and dx are the differentials of functions, and it makes sense to take their ratio. You ca
by mikebenfield 3y ago
Yes, it is possible to treat d as a differential operator, and then dy and dx are the differentials of functions, and it makes sense to take their ratio. You can learn about this by reading about differential forms:
https://en.wikipedia.org/wiki/Differential_form https://en.wikipedia.org/wiki/Differential_form
Unfortunately I don't know a treatment of this subject that explains how to apply this concept to basic calculus without introducing some other more difficult concepts.
- JBits 3y agoDifferential forms looks really cool and I really want to learn more about them at some point! That said, isn't calculus, mainly the chain rule, enough to tell you what operations are allowed?
- mikebenfield 3y agoI definitely didn't understand how to use differentials just by learning calculus, but maybe it is possible.
- lupire 3y agoFor single variable calculus (y=f(x)), yes.