3. Let $f(x, y) = \sqrt{1 + x^2 + y^2}$.
(a) Find the partial derivative $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$.
(b) Let $(a, b) \in \mathbb{R}^2$ and $c = f(a, b)$. Show that the vector $(-a, -b, c)$ is normal to the tangent plane to the surface $z = f(x, y)$ at the point $(a, b, c)$.
