let $a$ be a $c^*$-algebra, $f \colon \mathbb{r} \to \mathbb{c}$ be a continuous function, and $\tilde{f} \colon a_{\text{sa}} \to a$ be the functional calculus map $a_{\text{sa}} \ni a \mapsto f(a) \in a$. it is elementary to show that $\tilde{f}$ is continuous, so it is natural to wonder how the differentiability properties of $f$ relate/transfer to those of $\tilde{f}$. this turns out to be a delicate, complicated problem. in this talk, i introduce a rich class $nc^k(\mathbb{r}) \subseteq c^k(\mathbb{r})$ of noncommutative $c^k$ functions $f$ such that $\tilde{f}$ is $k$-times differentiable. i shall also discuss the interesting objects, called multiple operator integrals, used to express the derivatives of $\tilde{f}$.