A lot of results are available for the following chain-rule problem:

(CRP1) Let $ f\colon \mathbb R \to \mathbb R$ be a $ C^1$ /Lipschitz function and let $ g \colon \mathbb R^d \to \mathbb R$ be a weakly differentiable function (e.g. $ W_{\rm loc}^{1,p}$ or $ BV_{\rm loc}$ ). Then the function $ f \circ g$ is weakly differentiable as well and explicit chain rule formulas hold, like for instance in the Sobolev setting $ $ (f \circ g)'(x) = f'(g(x)) g'(x) $ $ a.e. with respect to Lebesgue measure (with some standards caveat when $ f$ is Lipschitz).

I am wondering for the other way round, i.e.

(CRP2) Let $ f\colon \mathbb R \to \mathbb R^d$ be a $ C^1$ /Lipschitz function and let $ g \colon \mathbb R^d \to \mathbb R$ be a weakly differentiable function (e.g. $ W_{\rm loc}^{1,p}$ or $ BV_{\rm loc}$ ). What can we say about the function $ g \circ f \colon \mathbb R \to \mathbb R$ ? For instance in the Sobolev setting it seems to me that the formula $ $ (g \circ f)'(x) = \nabla g(f(x)) \cdot f'(x) $ $ (a.e. with respect to Lebesgue measure) makes sense, doesn’t it? Are there any references about this topic?

Thanks.