In the Wikipedia article on the determinant, it is stated that
$$\det \left ( A + \epsilon X \right ) - \det \left ( A \right ) = {\rm tr} \left ( {\rm adj} \left ( A \right ) X \right ) \epsilon + {\rm O} \left ( \epsilon^2 \right )$$
where $A, X \in {\mathbb R}^{n \times n}$.
Any suggestions on how one might get to this?
Thanks!