Newtonian notation certainly feels more elegant to me. But kind of painful to work with in LaTeX. Langrangian notation is almost the same, and much eaiser to type too.
Newtonian notation is just doing time derivatives with a dot above them, so in Latex that is just \dot{x} = v . Which means dx/dt = v, or \ddot{x} = a.
Did you mean "Leibniz's" notation[1]? If so, if you use the esdiff package[2] it's just \diffp{y}{x} for partials or \diff{x}{y} for regular derivatives.
Lagrange's notation is when people do x' = v or x'' = a and Like the Newton's notation you kinda have to know from context that you are differentiating with respect to time unless they write it properly as a function with arguments which people often tend not to (at least I often tend not to I guess).
Sometimes people call the partial derivative notation where you use subscripts "Lagrange's notation" also[3]. So like f_x(x,y) = blah is the partial derivative of f with respect to x.
[1] Actually invented by Euler, or maybe some other guy called Arbogast or something[?sp]
It has been argued before [0] that Leibniz notation being embraced in mainland Europe and not adopted in England/UK was the reason England fell about a century behind. First heard of this in MIT Calc undergrad course on YouTube, but would be too tedious to find which video, hence ran a search on the Internet.
