My high school teacher always says that the (dy/dx) should not be interpreted as "dy" divided by "dx". (dy/dx) is a symbol meaning the derivative. However i often observed that mathematicians and physicists wrote such things as: dy=3dx instead of dy/dx=3 and even----(dy=3dx), divided by dt ,means (dy/dt=3dx/dt) ??????? Do they break the convention or my teacher is wrong ?