当然可以。改写 y = [f(x)]^g(x)为 y = e^g(x)lnf(x)，然后用复合函数求导法求导 y' = [e^g(x)lnf(x)]*[g(x)lnf(x)]' = [e^g(x)lnf(x)]*[g'(x)lnf(x)g(x)/f(x)]。
