Let $(V,0)\subset (\mathbb{C}^n,0)$, $n\geq 3$ a (germ of) hypersurface given by $V =\{f=0\}$, $f$ a germ of holomorphic function. A (germ of) holomorphic vector field $X$ on $(\mathbb{C}^n,0)$ is "tangent to $V$" if $X(f) = {\rm d}f(X)$ belongs to the ideal generated by $f$ in $\mathcal{O}_{\mathbb{C}^n,0}$.

My question is: **For any hypersurface germ $V$, does there exist a germ of vector field with an isolated singularity that is tangent to $V$?**

If $V$ is smooth or has an isolated singularity, this is fairly simple. However, for germs of non-isolated hypersurface singularities I could neither prove this nor find a counterexample.