Question

若f’’(x)存在,求下列函数的二阶导数d^2y/dx^2 :y=e^f(x)

Answer 1

ln(y)=f(x)

两边同时求导：

(1/y)*y'=f'(x)

y'=f'(x)*y

y'=e^f(x)*f'(x)

d^2y/dx^2=y''=e^f(x)*f'(x)*f'(x)+e^f(x)*f''(x)=e^f(x)*[(f'(x))^2+f''(x)]