16 Dec
2019
16 Dec
'19
8:55 a.m.
With[{r2x = 1/(1 - x*Cos[z])^2}, ReplaceAll[ Factor@Plus[ Dot[D[r2x, {x, #}] & /@ {0, 1}, {3 x, (x - 1) (x + 1)}], D[(2*Sin[z] - x*Cos[z] Sin[z]) r2x, z]], Sin[z]^2 -> 1 - Cos[z]^2]] This is no more fundamental a definition than the offering of yesterday; however, it may be easier to work with because r^2*dz is an area from, so A(x) = Pi/(1-x^2)^(3/2) , Should also follow from Cartesian definitions, i.e. from an x*dy integral of algebraic function. --Brad