Let \(\Omega\subseteq \mathbb{R}^d\) denote a domain, and let \( f : \Omega \to \mathbb{R} \) be differentiable. Then the gradient of \(f\) is defined by
\[ \grad f(x) = (\partial_1 f(x), \ldots , \partial_d f(x))\in \mathbb{R}^d. \]Sometimes, we write \(\nabla f\) instead of \(\grad f\).