Differentiate the functions given in w.r.t. x.
`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`.

Answer

`(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)]`

Explanation

`"Let "y=sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
Taking logarithm on both sides, we get
`log y = log sqrt(((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)]`
`(1)/(y)(dy)/(dx)=((1)/(x-1)+(1)/(x-2)-(1)/(x-3)-(1)/(x-4)-(1)/(x-5))`
`therefore" "(dy)/(dx)=(1)/(2)sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))xx`
`[(1)/(x-1)+(1)/(x-2)-(1)/(x-3)-(1)/(x-4)-(1)/(x-5)]`