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If `x^(2) = e^(x-y) `, then `(dy)/(dx)` at x = 1 is ……..A. eB. 1C. 0D. `-1` |
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Answer» Correct Answer - C Given have, `x^(y) = e^(x - y)` taking log on both sides, we get y logx = (x - y) log e = (x - y) When x = 1, then (log 1) = (1 - y) `implies y = 1` On differentiating both sides, `y((1)/(x)) + log x. (dy)/(dx) = 1 - (dy)/(dx)` `implies (dy)/(dx) (logx + 1) = 1 - (y)/(x)` `implies (dy)/(dx) (logx + 1) (x - y)/(x)` `implies (dy)/(dx) = ((x - y))/(x(logx + 1))` When x =1, then `((dy)/(dx)) = (1 -1)/(1(log1 +1)) = 0` |
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