Derivative symbol readability.

Written

I don't like the use of d to indicate total derivation. To me, it isn't really readable and although I haven't found it again I have seen an equation that mixed derivation and variable d. So I have been using the partial derivation symbol () even when the total derivation symbol would have been used. This works most of the time. Failure happens when the derivative is a composite function like particles movement in 3-dimensional space. V ( r(t) , t ) t = r ( t ) t V ( r(t) , t ) r + V ( r(t) , t ) t The second parameter's chain rule makes it look like the formula is recursive. This gets even more confusing if you use the lazy notation where you don't mark parameters as composite functions.

Hence I have to make some kind of marking difference. However, looking at standard notation styles there aren't much better notation styles. Euler's D is as bad as d. Euler's partial derivative uses xy which is more clear but confusion may rise to integrals so I would rather not use it. Newton's notion (a.) is too general and such it would be confusing to an outsider. Lagrange notation (f(n)) has some interesting application and if I need shorthands it is probably the best. The Problem is that partial derivative order isn't indicated.

The best notation style is still Leibniz's. How do I solve my problem? Well, I would say dividing between partial and total derivative is still bullshit. The difference is that in the other you don't need to care about composite functions (or it is assumed) but no definitional difference is given. So let's just use semi Leibniz's way to indicate function value after derivation to composite functions. So the particle example: V ( r(t) , t ) t = r ( t ) t V ( r(t) , t ) r + V ( x , y ) y | r(t) , t This fixes the recursive problem by making it clear that the derivation does not include the composite function.