Derivation of the derivative of a function from $f: \mathbb {R}(n\times m) \to \mathbb{R}$

Question

As I know about the derivations of derivatives, it turns out that derivatives are usually derived from the first-order Taylor expansion, concretely, $f(X + h) = f(X) + Dd(X)$ where $D$ is the derivative of $f$ with respect to $X$. But in this case, $f(X)$ is a scalar while $Dd(X)$ seems to be a matrix. Can anybody show me the appropriate Taylor expansion for this case or correct me if I'm wrong ? Thanks for help