Suppose we know Taylor's theorem for $f: \mathbb{R} \rightarrow \mathbb{R}$ with remainder. How would we use this to derive Taylor's theorem for $g: \mathbb{R}^2 \rightarrow \mathbb{R}$ with remainder?
To start, I'm trying to figure out which version of the 1-dimensional Taylor remainder to use (options are Lagrange, Cauchy, or integral form). To do this, I need to figure out the remainder for 2-variable Taylor. Wikipedia lists the remainder for a general n-variable Taylor's theorem, but I'm having trouble extracting the 2-dimensional case from it.