I am stuck on this question from a tutorial sheet I am going through.
Compute the mean and Gaussian curvature of a surface in $\mathbb{R}^3$ that is given by
$z=f(x)+g(y)$
for some good functions $f(x)$ and $g(y)$.
I tried calculating the first and second fundamental forms to then find $\kappa=\dfrac{det II}{det I}$ but it seems long and I feel like there should be an easier way. Also that doesn't tell me the mean curvature.