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

Options

A. `(1)/(t)`
B. `-1`
C. 1
D. t

Answer

D

Explanation

Given that , ` x = (1 + lot t)/(t^(2)) " and " y = (3 + 2 log t)/(t)`
On differentiating both functions w.r.t.t, we get
`(dx)/(dt) = (t^(2) .(1)/(t)-(1 + log t) 2t)/(t^(4))`
and ` (dy)/(dt) = (1 . (2)/(t)-(3 + 2 log t)xx1)/(t^(2))`
`rArr (dx)/(dt) = (t - 2t - 2t log t)/(t^(4)) " and " (dy)/(dt) = (2 - 3 - 2 log t)/(t^(2))`
`rArr (dx)/(dt) =- (1 + 2 log t)/(t^(3)) " and " (dy)/(dt) =- (1+ 2 log t)/(t^(2))`
`therefore (dy)/(dx)= (dy)/(dt).(dt)/(dx) =- (1 + 2 log t)/(t^(2)) xx(t^(3))/((1 + 2 log t))`
` rArr (dy)/(dx) = t `