Looking for a simplier expaination for the following:
Show the following for sub-gradients:
(a) If $g(x) = f(Ax + b)$, then $\delta g(x) = A^T \delta f(Ax + b)$.
I've found the trivial direction using the definition of a subgradient, but I don't really know where to begin finding the other direction.
I know I need to prove that $\delta g(x) \in A^T \delta f(Ax + b)$, thereby showing equality since they are both part of each other. I've read several breakdowns of how to do this and the special cases, but I don't fully understand them. Thanks!