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AP EAMCET2006MathematicsDifferential Equations

If x^y=y^x , then x(x-y x) d y d x is equal to :

Options

  1. Ay(y-x y)
  2. By(y+x y)
  3. Cx(x+y x)
  4. Dx(y-x y)

Correct answer

A. y(y-x y)

Step-by-step solution

x^y=y^x Taking log on both sides, we get y x=x y On differentiating with respect to x , we get y 1 x + x d y d x =x 1 y d y d x + y (x-y x) y d y d x = -x y+y x x(x-y x) d y d x =y(-x y+y)

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