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Find (dy)/(dx), when: xylog(x+y)=1...

Find `(dy)/(dx)`, when:
`xylog(x+y)=1`

Text Solution

Verified by Experts

The correct Answer is:
`(-(x+y+x^(2)y))/(x^(2){y+(x+y)log(x+y)})`
`ylog(x+y)=(1)/(x)`
`rArry.(1)/((x+y)).(1+(dy)/(dx))+log(x+y).(dy)/(dx)=(-1)/(x^(2))`
`rArr {(y)/((x+y))+log(x+y)}.(dy)/(dx)=-((1)/(x^(2))+(y)/(x+y)).`
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