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

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

Text Solution

Verified by Experts

The correct Answer is:
`(y(x-1))/(x(y+1))`
The given function is `xy=e^((x-y)).`
Taking logarithm on both the sides, we obtain
`log(xy)=log (e^(x-y))`
`log x + log y = (x-y)`
Differentiating both sides with respect to x, we get
`(1)/(x)+(1)/(y)(dy)/(dx)=1-(dy)/(dx)`
`"or "(1+(1)/(y))(dy)/(dx)=1-(1)/(x)`
`therefore" "(dy)/(dx)=(y(x-1))/(x(y+1))`
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