Hello,
Please I already open discussion and I got the great support and answer. However, here I add some information to code so I add new discussion. It is more complicated.
K(k) and E(k) are complete elliptical integral kind one and two. both are function of (y and r) (U) is also function of (y and r) because it have K(k),k, and E(k)
R and Y are constant
I am trying to get Ur which is partial derivative of U with respect to y. and Uy which is partial derivative of U with respect to r.
I tried these steps but it doesn't getting through.
k = ((4*R*r)/((y - Y)^2 + (r + R)^2))^1/2;
A[k_] := EllipticK[k];
B[k_] := EllipticE[k];
U = (R*r)^1/2/(2*Pi*k) ((2 - k^2)*A[k] - 2*B[k]),
Ur = [(1/r) (D[U]), y]
Uy = [(-1/r) (D[U]), r]
Thanks