`(dy)/(dx)` ज्ञात कीजिए ।
`y^(x)=x^(y)`

Explanation

`y^(x)=x^(y)`
`rArr" "log(y^(x))=log(x^(y))`
`rArr" "xlogy=ylogx`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
`x.(d)/(dx)logy+logy.(d)/(dx)x`
`y.(d)/(dx)logx+logx.(d)/(dx)y`
`rArr" "(x)/(y)(dy)/(dx)+logy.1=(y)/(x)+logx(dy)/(dx)`
`rArr" "((x)/(y)-logx)(dy)/(dx)=(y)/(x)+logx(dy)/(dx)`
`rArr" "(x-ylogx)/(y)(dy)/(dx)=(y-xlogy)/(x)`
`rArr" "(dy)/(dx)=(y)/(x).(y-xlogy)/(x-ylogx)`