Find the two variable Maclaurin series for $f(x,y) = e^{x+y}$ I'm shaky with Taylor/Maclaurin series, and I've been over and over my book and notes and still feel like I'm at square one...

You can write $f(x,y) = f(x+y,0) = \sum_{n=0}^\infty \frac{(x+y)^n}{n!} = \sum_{n=0}^\infty \sum_{k=0}^n \frac{1}{n!} \binom{n}{k} x^k y^{n-k}$.
From this, we can read off the $x^i y^j$ term coefficient as $\frac{1}{(i+j)!} \binom{j+i}{i} = \frac{1}{i!} \frac{1}{j!}$ (by letting $(i,j) = (k,n-k)$ and solving for $k,n$ in terms of $i,j$).
