Let $f, f_1, f_2 : \mathbb{R}^d \to \mathbb{R}$ be convex. Then: **(i)** For $\alpha > 0$: $\partial(\alpha f)(x) = \{\alpha g : g \in \partial f(x)\}$. **(ii)** $\partial(f_1 + f_2)(x) = \{g_1 + g_2 : g_1 \in \partial f_1(x),\, g_2 \in \partial f_2(x)\}$. **(iii)** If $h : \mathbb{R}^m \to \mathbb{R}$ is defined by $h(x) = f(Ax + b)$ for $A \in \mathbb{R}^{d \times m}$ and $b \in \mathbb{R}^d$, then \begin{align*} \partial h(x) = \{A^\top g : g \in \partial f(Ax + b)\}. \end{align*}