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"If "xy=e^((x-y))," then find "(dy)/(dx)...

`"If "xy=e^((x-y))," then find "(dy)/(dx).`

Text Solution

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`xy = e^(x-y) " "....(1)`
Differentiate both sides w.r.t.x
` x(dy)/(dx) + y * 1 = (d)/(dx)e^((x-y))`
`rArr x(dy)/(dx) + y = e^((x-y)) * (d)/(dx) (x-y)`
`rArr x(dy)/(dx) + y = xy(1-(dy)/(dx)) " From equation" (1)`
`rArr x(dy)/(dx) + xy(dy)/(dx) = xy-y`
`rArr (dy)/(dx) = (y(x-1))/(x(1+y))`
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