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
$z = f(u(t),v(t))$ 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