Question

if u=x/√(1-r²),v=y/√(1-r²),w=z/√(1-r²),,where r²=x²+y²+z² then find
J{(u,v,w)/(x,y,z).

Answer 1

\[\Large J=\left|\begin{array}{ccc}\frac{\partial u}{\partial x} & \frac{\partial u}{\partial y} & \frac{\partial u}{\partial z}\\\frac{\partial v}{\partial x} & \frac{\partial v}{\partial y} & \frac{\partial v}{\partial z}\\\frac{\partial w}{\partial x} & \frac{\partial w}{\partial y} & \frac{\partial w}{\partial z}\\\end{array}\right|\]