Derivative of Matrix Exponential

Theorem
Let $\mathbf A$ be a square matrix.

Let $t \in \R$ be a real number.

Let $e^{\mathbf A t}$ denote the matrix exponential of $\mathbf A$.

Then:
 * $\dfrac \d {\d t} e^{\mathbf A t} = \mathbf A e^{\mathbf A t}$