If `x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\ \ ` find `(dy)/(dx)` .

Answer

N/a

Explanation

`:' x = (1+logt)/(t^(2))` and `y = (3+2logt)/(t)`
` :. (dx)/(dt) = (t^(2).(d)/(dt)(1+logt)-(1+logt).(d)/(dt)t^(2))/((t^(2))^(2))`
`=(t^(2).(1)/(t)-(1+logt).2t)/(t^(4))= (t-(1+logt).2t)/(t^(4))`
`= (t)/(t^(4)) [1-2(1+logt)]= (-1-2logt)/(t^(3))"...."(i)`
`=(t.2.(1)/(t)-(3+2logt).t)/(t^(2))`
and `(dy)/(dt) = (t.(d)/(dt)(3+2logt)-(3+2logt).(d)/(dt)t)/(t^(2))`
`= (t.2.(1)/(t)-(3+2 logt).1)/(t^(2))`
`= (2-3-2logt)/(t^(2))= (-1-2logt)/(t^(2))"....."(ii)`
`:. (dy)/(dx)= (dy//dt)/(dx//dt) = (-1-2logt//t^(2))/(-1-2logt//t^(3)) = t`