Let \(\Omega\) denote a domain on \(\mathbb{R}^n\), and \(F\colon \Omega\to \mathbb{R}^m\) is a differentiable Lipschitz function. Then \(\sup_{x\in \Omega}\lVert DF(x)\rVert\) is a Lipschitz constant of \(F\). In particular, \(\sup_{x\in \Omega}\lVert DF(x)\rVert\) is bounded.