Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

Please help me with partial differentiation with the propagation of errors. I need to find the error in A where B, U, D are all independent variables, for this equation A = (1/2)*arcsin(B/U)-(1/2)*arcsin(B/D)

FYI, A is the dip angle, B is velocity in layer 1, D is the down velocity and U is the up velocity. This work is about seismic refraction.

I know the values for the errors in B, U, D (which I shall call b, u and d) and I have values for the variables themselves. I need a solution for the error in A, which I shall call a.

I think partial differentiating B, U and D with respect to A gives A = 1/(2*U*sqrt(1-B^2/U^2))-1/(2*D*sqrt(1-B^2/D^2)) + (1/2)*B/(D^2*sqrt(1-B^2/D^2)) -(1/2)*B/(U^2*sqrt(1-B^2/U^2))

Although I need it in the format of standard deviations like shown on this web page Uncertainties and Error Propagation which I think should be a fractional error with the error "a" divided by "A", i.e.
(a/A)^2 = ((1/(2*U*sqrt(1-B^2/U^2))-1/(2*D*sqrt(1-B^2/D^2)))*b/B)^2 + (((1/2)*B/(D^2*sqrt(1-B^2/D^2))*d/D)^2 + ((1/2)*B/(U^2*sqrt(1-B^2/U^2)))*u/U)^2

Please can someone help make this clearer for me as I am not sure if I've gone off on a tangent! (poor maths joke)

I need to get this completed within the next 48 hrs.