Answer the following for the surface $z = f(x, y)$ defined implicitly with $2yz + 2 = \ln (x + z)$.
- Find the equation of the tangent plane to the surface at $(2, 1, 1)$.
- Identify a normal vector of the tangent plane found in 1. above.
- Find the linearization $L(x, y)$ for $(x, y)$ near $(2, 1)$.
- Use $L(x, y)$ found above to approximate $f(1.98, 1.02)$.
I need to start by finding the partial derivatives with respect to $x$ and $y$ before I can do anything else. How do I do this?