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Choose the correct option from the given alternatives : If xy = yx, then dydx = ..........

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Question

Choose the correct option from the given alternatives :

If xy = yx, then `"dy"/"dx"` = ..........

Options

  • `(x(xlogy - y))/(y(ylogx - x)`

  • `(y(xlogy - y))/(x(ylogx - x)`

  • `(y^2(1 - logx))/(x^2(1 - logy)`

  • `(y(1 - logx))/(x(1 - logy)`

MCQ
Sum
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Solution

`(y(xlogy - y))/(x(ylogx - x)`

xy = yx    ∴ y log x = x log y

`∴ y xx (1)/x + (logx)"dy"/"dx" = x xx (1)/y"dy"/"dx" + logy`

`∴ (log x - x/y)"dy"/"dx" = logy - y/x`

`∴ ((ylog x - x)/y)"dy"/"dx" = (xlogy - y)/x`

`∴ "dy"/"dx" = (y(xlogy - y))/(x(ylogx - x))`.

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Chapter 1: Differentiation - Miscellaneous Exercise 1 (I) [Page 62]

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