这个题怎么求二阶导数。。
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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]
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