Use implicit differentiation and logaritmic differentiation.

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Use implicit differentiation and logaritmic differentiation.

[From: ] [author: ] [Date: 11-06-15] [Hit: ]

Find y' if x^y=y^x

The answer is:(lny-(y/x))/(lnx-(x/y))

How does this happen?

Take log on both sides

y lnx = x lny
y' lnx + y/x = lny + xy'/y

y' (lnx - x/y ) = lny - y/x

Thus y' = (lny-(y/x))/(lnx-(x/y))

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