I have the following implicit equation as functions of x and y:

xu+yv+(u^2)-(v^2)-1=0

2xyuv-1=0

I found using Jacobian matrices etc. that the partial derivative of u with respect to x is:

-u(xu-yv+(2v^2))/(x(xu+(2u^2)-yv+(2v^2))

How do you find the partial derivative of this (ie the second partial derivative d^2u/dx^2, the second partial derivative of u with respect to x)?

Thank you for any help or clarification.