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MHT CET202122 Sep 2021Evening ShiftMathematicsDifferentiationActual

If x^y y^x=16 , then d y d x at (2,2) is

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

A. -1

Step-by-step solution

x^y y^x=16 Taking on both sides, y x + x y = 16 Differentiating w.r.t. x, y x +( x) d y d x + ( x y ) d y d x + y=0 aligned & [ x+ x y ] d y d x =- [ y x + y ] & d y d x = - [ y x + y ] [ x+ x y ] ( d y d x )_ (2,2) =- [ (1+ 2) 2+1 ]=-1 aligned

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