Differentiability
= Differentiability
Differentiability is the existence of a <derivative> at a point. For maps between finite-dimensional <normed vector spaces>, the existence of a <Frechet derivative> requires a single <linear map> approximating the increment with error $o(\|h\|)$. Merely having <partial derivatives> need not provide this approximation; <continuous> <partial derivatives> on a neighbourhood do suffice.