Say [x,y,z] and [r,?,z] represents Cartesian and Cylindrical co-ordinate system. Hence x & y both are functions of (r,?). Let p is function of (x, z) only and D[p, y] = 0. How should I represent them in sequence?

If I write

p = Function[{x, z}]

then

D[p, x] and D[p, z] give results '{1, 0} &' and '{0, 1} &'

But if I write like following

x = Function[?]

p = Function[{x, z}]

then though D[p, z] gives output '{0, 1} &', but D[p, x] and D[p, ?] gives output '{0, 0} &' and '{0, 0} &'

Please explain me.

During the solution of a hydrodynamic journal bearing problem following Reynold's approach all coefficients, intermediate expressions and final expressions of velocity components along x- and z-directions absolutely match with my manual derivation. However, D[Vx, y] is returning an extra term associated to '({0, 0} &)', which I suspect to be associated with D[(D[p, x]), y]. Why does it remain when p is not a function of y? How do I eliminate that term?