Distribution and convolutions [closed]

Let $f(x,y)=y^2\chi_E(x,y)$ with $E= \{ (x,y) \in \mathbb{R}^2 s.t. x\ge 0\}$, let $B$ the unit ball in $\mathbb{R}^2$ and let $\{\rho_\epsilon \} $ standard mollifier.

I should compute $\lim_{\epsilon\to 0} \left \langle \frac{\partial f}{\partial x}, \rho_\epsilon * \chi_B \right \rangle$, I tried but I was not successful. Can someone please help me?