घनात्मक अचर के लिए`(dy)/(dx)` ज्ञात कीजिए , जहाँ ` y = a^(t+1/t)` तथा ` x = ( t + 1/t)^(a)`.

Explanation

` :' y = a^(t + 1/t)`
` :. (dx)/(dt) = a ^(t+1/t) log a. d/(dt) (t +1/t)`
` = a^(t+1/t) loga `
तथा ` x = (t+1/t)^(a)`
` :. (dx)/(dt) = a. ( t+1/t)^(a) `
` = a (t+1/t) ^(a-1) (1-1/t^(2))`
अब ` (dy)/(dx) = (dy//dt)/(dx//dt) `
` = (a^(t+1/t) .log.a.(1-1/t^(2)))/(a(t+1/t) ^(a-1).(1 -1/t^(2)))`
` = ( a^(t+1/t) .loga)/(a (t + 1/t)^(a-1))`