Chain Rule

Total Derivative

$z=f(u(t),v(t))$ where $v=v(t),u=u(t)$
$\frac{df}{dt}=\frac{dz}{dt}=f_u\frac{du}{dt}+f_v\frac{dv}{dt}$
换元法：换元后求二阶偏导数
Partial Derivative