  We consider a two-parameter family of maps $T_{\alpha, \beta}: [0,1] \to
[0,1]$ with a neutral fixed point and a non-flat critical point. Building on a
cone technique due to Baladi and Todd, we show that for a class of $L^q$
observables $\phi: [0,1] \to \mathbb{R}$ the bivariate map $(\alpha, \beta)
\mapsto \int_0^1 \phi \, d\mu_{\alpha,\beta}$, where $\mu_{\alpha, \beta}$
denotes the invariant SRB measure, is differentiable in a certain parameter
region, and establish a formula for its directional derivative.
