设f''(x)存在,求下列函数的二阶导数d^2y/dx^21.y=f(x) 2.y=ln[f(x)]
问题描述:
设f''(x)存在,求下列函数的二阶导数d^2y/dx^2
1.y=f(x) 2.y=ln[f(x)]
答
(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)