Let $f \in \mathbb{C}[x,y,z]$ be a polynomial which defines an isolated singularity $0 \in D:= (f=0) \subset \mathbb{C}^3$. Assume that $\mathcal{D}:= (f+tx =0) \subset \mathbb{C}^3 \times \mathbb{C}$ defines a smoothing of $D$ over a small disk. Let $g \in \mathbb{C}[x,y,z]$ be a polynomial which has a zero of order $\ge 2$ at $0$.

**Question**
Let $\mathcal{D}' := (f+t(x+g)=0)$ be a deformation of $D$ induced by $x+g$.
Is $\mathcal{D}'$ smoothing?