數學物理證明題

d{f(t) + g(t)}/dt = df(t)/dt + dg(t)/dt...分配率

d{f(t) g(t)}/dt = f(t) {dg(t)/dt} + {df(t)/dt} g(t)

If f(t) = g(u(t)), then:
=> df(t) / dt = [df(t)/du(t)] [du(t)/dt] = [dg(u) / du(t)][du(t)/dt]...連鎖率

Question: Prove the formula.