这个题怎么求二阶导数。。
展开全部
y^(1/x) = x^(1/y)
取对数
(lny)/x = (lnx)/y
ylny = xlnx
d(ylny) = d(xlnx)
(lny)dy + y(1/y)dy = (lnx)dx + x(1/x)dx
(lny)dy + dy = (lnx)dx +dx
dy/dx = (lny + 1) / (lnx + 1)
y' = (lny + 1) / (lnx + 1)
y'' = [(1/y)y'(lnx + 1) - (1/x)(lny + 1)] / (lnx + 1)^2
= [(lny + 1)/y - (lny + 1)/x] / (lnx + 1)^2
= [(lny + 1)(x - y)]/[xy(lnx + 1)^2]
取对数
(lny)/x = (lnx)/y
ylny = xlnx
d(ylny) = d(xlnx)
(lny)dy + y(1/y)dy = (lnx)dx + x(1/x)dx
(lny)dy + dy = (lnx)dx +dx
dy/dx = (lny + 1) / (lnx + 1)
y' = (lny + 1) / (lnx + 1)
y'' = [(1/y)y'(lnx + 1) - (1/x)(lny + 1)] / (lnx + 1)^2
= [(lny + 1)/y - (lny + 1)/x] / (lnx + 1)^2
= [(lny + 1)(x - y)]/[xy(lnx + 1)^2]
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
