Jacobi’s formula says: $\frac{d}{dt}\text{det}(A(t))=\text{det}(A(t)) \cdot \text{tr}(\text{Ad}(A(t))\cdot\frac{d}{dt}(A(t))$.
Exists maybe a variation of the Jacobi’s formula where $\text{det}(\frac{d}{dt}(A(t))$ is involved (For a relation between $\frac{d}{dt}\text{det}(A(t))$, $\text{det}(A(t))$ and $\text{det}(\frac{d}{dt}(A(t))$?
