Unique competitive equilibrium in an exchange economy

I was working on the following excercise:

In an exchange economy $varepsilon$ with two goods and strictly monotone, continous and strict concave utility functions, suppose all demand functions are differentiable. (This means that the aggregate excess demand map $z(1,p_2):mathbb{R}rightarrowmathbb{R^2_{++}}$ is differentiable)

I need to prove that at a competitive equilibrium, say $((1,overline{p_2 }),(overline{x_i})_{iin I})$, if this equilibrium is unique, we have
$$ frac{delta z_2}{delta p_2} (1, overline{p_2}) le0$$

I would appreciate any hint! Thank you.