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Question

If xy=ex-y, find dydx.

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Solution

We have, xy=ex-y
Taking log on both sides,
logxy=logex-ylogx+logy=x-ylogelogx+logy=x-y×1logx+logy=x-y

ddxlogx+ddxlogy=ddxx-dydx1x+1ydydx=1-dydx1+1ydydx=1-1xy+1ydydx=x-1xdydx=yx-1xy+1

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