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99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

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

Options

  1. Ay(x x y+ y) x( x-y x y)
  2. By(x x x- y) x( x+y x y)
  3. Cy( y-x y) x(x-y y( x))
  4. Dy( y+x y) x(x+y y( x))

Correct answer

A. y(x x y+ y) x( x-y x y)

Step-by-step solution

It is given that y^ x =x^ y On taking logrithm both sides, we get x y= y x On differentiating both side w.r.t. x , we get 1 y ( x) d y d x -( x) y= 1 x y+( x)( y) d d x aligned & d y d x ( 1 y x-( x) y )= 1 x y+( x) y & d y d x = y( y+x x y) x( x-y x y) aligned

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