1.

`sqrt((x+1)(x+2)(x+3))` का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए ।

Answer» माना `y=sqrt((x+1)(x+2)(x+3))`
`rArr" "logy=log[sqrt((x+1)(x+2)(x+3))]`
`" "=(1)/(2)log[(x+1)(x+2)(x+3)]`
`" "=(1)/(2)[log(x+1)+log(x+2)+log(x+3)]`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
`" "(1)/(y)(dy)/(dx)=(1)/(2)[(1)/(x+1)+(1)/(x+2)+(1)/(x+3)]`
`rArr" "(dy)/(dx)=(1)/(2)y((1)/(x+1)+(1)/(x+2)+(1)/(x+3))`
`" "=(1)/(2)sqrt((x+1)(x+2)(x+3))`
`" "((1)/(x+1)+(1)/(x+2)+(1)/(x+3))`


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