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Differentiate sqrt(((x-1)(x-2))/((x-3)(x...

Differentiate `sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))` with respect to `x`

Text Solution

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`"Let "y =sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
`rArr "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)]`
Differentiate both sides w.r.t.x.
`(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)}`
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