Property of derivative of Dirac delta function in $\mathbb{R}^n$

Question

With reference to Property of Dirac delta function in $\mathbb{R}^n$, is there a similar formula for $\langle g^*\delta', f \rangle$ (or even $\langle g^*\delta^{(n)}, f \rangle$)? By similar I mean a representation by an integral over $g^{-1}(0)$.