If then x y = e x - y , then d y d x at x =1 is ….

Question

If then x y = e x - y , then d y d x at x =1 is …., e, 1, 0, -1

MARKS App · Accepted Answer

Given have, x y = e x - y taking log on both sides, we get y l o g x = x - y l o g e = x - y ….(i) when x = 1 , t h e n y l o g 1 = 1 - y ⇒ y = 1 On differentiating both sides, y 1 x + l o g x . d y d x = 1 - d y d x ⇒ d y d x l o g x + 1 = 1 - y x ⇒ d y d x l o g x + 1 = x - y x ⇒ d y d x = x - y x l o g x + 1 when x = 1, then d y d x = 1 - 1 1 l o g 1 + 1 = 0

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