The system of equations:
$x-u^2-v^2+9=0$
$y-u^2+v^2-10=0$
defines $(u,v)$ as a function of $(x,y)$ in every point $u\cdot v\ne 0$
I wish to find $u_{xx}$
I managed to find $u_x$:
if $F=(x-u^2-v^2+9,y-u^2+v^2-10)$ than $u_x=\frac{\partial u}{\partial x}=\frac{1}{4u}$
but i have no idea how to find the second derivative.
any ideas? (the answer is $-\frac{1}{16u^3}$)
Well $$ u_{xx}=\frac{\partial}{\partial x}u_x=\frac{\partial}{\partial x}\frac{1}{4u}=-\frac{1}{4u^2}u_x=-\frac{1}{16u^3} $$