I’ll try to dig out Griffith for a better explanation but has to do with the fact that when you do a partial derivative you kinda lose information I guess?

(Idk, this is heady trying to make math into reality shit and I got a “c” in the class (for reasons partially related to other things) - also, there might be a way to do latex in markdown but I’m a bit too stoned to figure out)

So go back how often we do implicit differential because it’s just an opportunity to look at how sexy the chain rule is. d(xy)/dx = xy’+x’y god fucking dammit that gorgeous

But okay. Think about position and velocity. Velocity is the derivative of position right (and also connected to energy - KE = 1/2mv^2 and E = mc^2 lol)

But since velocity is a derivative of position, it loses information. d(mx+b)/dx turns into m, no way to ever get b back with an initial value condition.

Then - omigod, when you take a partial - you have to ignore dependence. curlyd(xy+by)/curlydx turns into y and then things is really fucked if there was any dependence on y.

There are some operators that are just exclusionary. Once you chose to look for one, you’ve discounted the chance of finding the other.