About Subdifferential of matrix norm

Question

We have the definition of subdifferential of convex function $f : X \to R$ (where $X$ is complex Banach space) at a point $x \in X$ is set of linear function $v^*\in X^*$ such that $$f (y) − f (x) \geq Re \ v^∗(y−x)$$ and set of subdifferential is denoted by $\partial f(x)$ at point $x$. Then how to find $\partial\|A\|$ where A is $n\times n$ complex matrix. Since norm is convex function so can find $\partial\|A\|$. Here norm of $A$ is operator norm.