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KCET2007MathematicsDifferentiation

If x^ x =y^ y , then d y d x is

Options

  1. A- y x
  2. B- x y
  3. C1+ ( x y )
  4. D1+ x 1+ y

Correct answer

D. 1+ x 1+ y

Step-by-step solution

Given, x^ x =y^ y Taking log on both sides, we get x x=y y Differentiating w.r.t. y , we get aligned &y 1 y d y d x + y d y d x =x 1 x + x & d y d x (1+ y)=1+ x & d y d x = 1+ x 1+ y aligned

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