Let U⊂RnU \subset \mathbb R^nU⊂Rn be open. The partial derivative of a function f:U→Rmf:U\to\mathbb R^mf:U→Rm with respect to the iiith coordinate xix_ixi at a=(a1,…,an)∈Ua = (a_1,\dots,a_n) \in Ua=(a1,…,an)∈U is defined as ∂f∂xi(a)=limh→0f(a1,…,ai+h,…,an)−f(a)h.\frac{\partial f}{\partial x_i}(a) = \lim_{h\to 0} \frac{f(a_1,\dots,a_i+h,\dots,a_n) - f(a)}{h}.∂xi∂f(a)=h→0limhf(a1,…,ai+h,…,an)−f(a).
Wikidata ID: Q186475