I am solving the absolute condition for a problem $f(\vec{x})$. The definition is clear, $K_{abs}$ is the minimal number greater zero such that $|| f(\vec{x}) - f(\tilde{\vec{x}}) || \leq K_{abs} || \vec{x} -\tilde{\vec{x}}||$
Now I also found that I can just compute it as $K_{abs} = || f'(\vec{x}) ||$
How does it follow from the definition? Specifically, is it valid for any differentiable $f$ (also nonlinear)?