1. ## implicit differentiation

How do you show that these equations
$x^2 - y\cos(uv)+z^2 =0$
$x^2 + y^2 - \sin(uv)+2z^2 =2$
$xy-\sin(u) \cos(v) +z=0$
determine x,y and z as functions of (u,v) when (u,v,x,y,z) is close to $(\frac{\pi}{2}, 0,1,1,0)$

2. Use the Implicit function theorem - Wikipedia, the free encyclopedia

So start by taking all the partial derivatives.