If `y = sqrt(((x-a)(x-b))/((x-c)(x-d))), " then " (dy)/(dx)` is equal to

Options

A. `y/2 =[(1)/(x-a) + (1)/(x-b) - (1)/(x-c) - (1)/(x-d)]`
B. `y =[(1)/(x-a) + (1)/(x-b) - (1)/(x-c) - (1)/(x-d)]`
C. `1/2 =[(1)/(x-a) + (1)/(x-b) - (1)/(x-c) - (1)/(x-d)]`
D. None of above

Answer

A

Explanation

Given `y = sqrt(((x-a)(x-b))/((x-c)(x-d)))`
On takting log both sides , we get
`(1)/(y)(dy)/(dx) = (1)/(2) [(1)/(x-a) + (1)/(x-b) - (1)/(x-c) - (1)/(x-d)]`
`rArr (dy)/(dx) = (y)/(2) [(1)/(x-a) + (1)/(x-b) - (1)/(x-c) - (1)/(x-d)]` .