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NDA2022MathematicsDifferentiationActual

If x^y y^x=1 , then what is d y d x at (1,1) equal to?

Options

  1. A-1
  2. B0
  3. C1
  4. D4

Correct answer

A. -1

Step-by-step solution

x ^ y y ^ x =1 Taking log both sides aligned & y x+x y=0 & y^ x+ y x + y+ x y y^ =0 aligned put x =1, y =1 aligned & y ^ (1)+1+ (1)+ y ^ =0 & 0+1+0+ y ^ =0 y ^1=-1 aligned

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