備忘録~行列・行列式の微分~

$$\begin{array}{rcl} \frac{\partial}{\partial u}\det \qty(\begin{array}{cc} f_1 & f_2\\ g_1 & g_2 \end{array}) &=& \frac{\partial}{\partial u}(f_1g_2-f_1g_1)\\ &=& \det \qty(\begin{array}{cc} \frac{\partial}{\partial u}(f_1 & f_2)\\ g_1 & g_2 \end{array})+\det \qty(\begin{array}{cc} f_1 & f_2\\ \frac{\partial}{\partial u}(g_1 & g_2) \end{array}) \end{array}$$