`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`

Explanation

माना `y=sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
`rArr" "logy=logsqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
`=(1)/(2)[log(x-1)+log(x-2)-log(x-3)-log(x-4)-log(x-5)]`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
`(1)/(y)(dy)/(dx)=(1)/(2){(1)/(x-1)+(1)/(x-2)-(1)/(x-3)-(1)/(x-4)-(1)/(x-5)}`
`rArr" "(dy)/(dx)=(1)/(2)sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
`{(1)/(x-1)+(1)/(x-2)-(1)/(x-3)-(1)/(x-4)-(1)/(x-5)}`