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

Explanation

`(cosx)^(y)=(cosy)^(x)`
`rArr" "log(cosx)^(y)=log(cosy)^(x)`
`rArr" "ylog cos x=x log cos y`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
`y.(d)/(dx)log cos x+log cos x (d)/(dx)y`
`=x(d)/(dx)log cos y+log cos y (d)/(dx)x`
`rArr" "y.((-sinx))/(cosx)+log cos x. (dy)/(dx)`
`=(x(-siny))/(cosy)(dy)/(dx)+log cos y.1`
`rArr" "-y tan x+log cos x(dy)/(dx)`
`=-x tany (dy)/(dx)+log cos y`
`rArr" "(log cos x+x tany)(dy)/(dx)=log cos y+y tanx`
`rArr" "(dy)/(dx)=(logcos y+y tanx)/(log cos x+x tany)`