Derivative of a matrix valued function involving Hadamard product and SVD

Question

Consider a map $f:\mathcal{V}_m(\mathbb{R}^n)\times\mathbb{R}^m\times \mathcal{O}(m)\to \mathbb{R}^{n\times m}$ given by:
$$f(U,D,V)=A\circ UDV^T+UDV^T,$$ where $U^TU=I_m$, $V^TV=I_m$, $D$ is a diagonal matrix of singular values, $A$ is a fixed $n\times m$ matrix with entries 0 and 1, and $\circ$ denotes the Hadamard product of two matrices. Given that the map is totally differentiable, what is its Jacobian?