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If x^y=y^x ,"then find"(dy)/(dx)dot...

If `x^y=y^x ,"then find"(dy)/(dx)dot`

Text Solution

Verified by Experts

The correct Answer is:
`(y(x log y-y))/(x(y log x -x))`
`y^(x)=x^(y)`
`"or "log y^(x)= log x^(y)`
`"or "x log y = y log x`
`"or "x(1)/(y)(dy)/(dx)+log y xx1 =(y)/(x)+log x (dy)/(dx)`
`"or "((x)/(y)-log x)(dy)/(dx)=(y)/(x)-log y`
`"or "(dy)/(dx)=(y/x-logy)/((x)/(y)-log x)=(y(y-x log y))/(x(x- y log x))=(y(x log y - y ))/(x(y log x -x))`
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