大学高数:函数y=f(x)的导数f'(x)与二阶导数f''(x)存在且不为零,其反函数为x=u(y),则u''(y)等于……我的答案是-f''(x)/[f'(x)]2(平方)而答案是-f''(x)/[f'(x)]3(立方),
问题描述:
大学高数:函数y=f(x)的导数f'(x)与二阶导数f''(x)存在且不为零,其反函数为x=u(y),则u''(y)等于……
我的答案是-f''(x)/[f'(x)]2(平方)而答案是-f''(x)/[f'(x)]3(立方),
答
u'(y)=1/f'(x)=1/f'(u(y))
u''(y)=(1/f'(u(y)))'=-1/(f'(x))^2 * f''(x) * u‘(y) (复合函数求导)
=-f''(x)/(f'(x))^2 * 1/f'(x)
=-f''(x)/(f'(x))^3