Can’t you just use infinitesimals and then actually multiply them? It never results in an invalid operation with the normal dx, only the one with the fancy d (forgive my lack of terminology knowledge)
In (d/dx)f(x), d/dx is a symbol that means the derivative of f with respect to x. It’s not a division of two variables. But, the reason the symbol is useful is that you sort of can multiply the dx in some situations.
I understand that it’s a symbol, not a fraction, and that the top and bottom are linked and not separable. But, you can also use an equivalent infintesimal fraction dy/dx with the actual infintesimal values dy and dx being manipulatable. If I’m wrong, you’ll be able to find an example that doesn’t work (without using partial derivatives-- those actually can’t be cancelled).
Can’t you just use infinitesimals and then actually multiply them? It never results in an invalid operation with the normal dx, only the one with the fancy d (forgive my lack of terminology knowledge)
In (d/dx)f(x), d/dx is a symbol that means the derivative of f with respect to x. It’s not a division of two variables. But, the reason the symbol is useful is that you sort of can multiply the dx in some situations.
I understand that it’s a symbol, not a fraction, and that the top and bottom are linked and not separable. But, you can also use an equivalent infintesimal fraction dy/dx with the actual infintesimal values dy and dx being manipulatable. If I’m wrong, you’ll be able to find an example that doesn’t work (without using partial derivatives-- those actually can’t be cancelled).