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Differentiate the functions given w.r.t....

Differentiate the functions given w.r.t. x:`(x+3)^2dot(x+4)^3dot(x+5)^4`

Text Solution

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`"Let "y = (x + 3)^(2) * (x + 4)^(3) * (x + 5)^(4)`
`"log "y ="log "{(x + 3)^(2)(x + 4)^(3)(x + 5)^(4)}`
`= 2 "log" (x+3) + 3 "log" (x+4) + 4"log" (x+5)`
Differentiate both sides w.r.t.x
`(1)/(y)(dy)/(dx)= (2)/(x+3)+(3)/(x+4)+(4)/(x+5)`
`rArr (dy)/(dx) = y [(2)/(x+3)+(3)/(x+4) + (4)/(x+5)]`
`rArr (dy)/(dx) = (x+3)^(2)(x+4)^(3)(x+5)^(4)[(2)/(x+3) + (3)/(x+4) + (4)/(x+5)]`
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