设f✀✀(x)存在,求下列函数的二阶导数d^2y⼀dx^2

1.y=f(x) 2.y=ln[f(x)]
2025-01-20 13:21:59
推荐回答(1个)
回答1:

(1)
y=f(x)
d^2y/dx^2
=d(f'(x))/dx
=f''(x)

(2)
y=ln[f(x)]
dy/dx
=f'(x)/f(x)
d^2y/dx^2
=d[f'(x)/f(x)]/dx
=[f''(x)f(x)-f'(x)f'(x)]/f^2(x)
=(f''(x)f(x)-[f'(x)]^2)/f^2(x)