real analysis - A bound for the product of two functions in $H^1$

Question

Let $B$ be the unit ball in $\mathbb R^2$, and $f: B\rightarrow \mathbb R,\;\;(y_1,y_2)\mapsto \frac{1}{\sqrt{1-y_1^2}}$, and $\eta \in \mathcal D(B)$.

I would like to prove that there is a constant such that:

$\left \| f \eta \right \|_{H^1(B)}\leq c \left \| \eta \right \|_{H^1(B)}$.

I would greatly appreciate your help.

EDIT: $\mathcal D(B)$ are the compactly supported smooth functions on $B$.