1.

Differentiate `sqrt((x+1)(x+2)(x+3))` with respect to x.

Answer» Let y=`sqrt((x+1)(x+2)(x+3))`
`rArrlogy=log[sqrt((x+1)(x+2)(x+3))]`
`=1/2log[(x+1)(x+2)(x+3)]`
`=1/2[log(x+1)+log(x+2)+log(x+3)]`
Differentiate both sides with sides with respect to x
`1/y(dy)/(dx)=1/2[1/(x+1)+1/(x+2)+1/(x+3)]`
`rArr(dy)/(dx)=1/2y(1/(x+1)+1/(x+2)+1/(x+3))`
`=1/2sqrt((x+1)(x+2)(x+3))`
`(1/(x+1)+1/(x+2)+1/(x+3))`. Ans


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