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MHT CET2012MathematicsDifferentiation

If x^ p +y^ q =(x+y)^ p+q , then d y d x is

Options

  1. A- x y
  2. Bx y
  3. C- y x
  4. Dy x

Correct answer

D. y x

Step-by-step solution

If x^ p +y^ q =(x+y)^ p+q Taking log on both sides, p x+q y=(p+q) (x+y) On differentiating w.r.t x , we get p x + q y d y d x = (p+q) (x+y) (1+ d y d x ) p x - p+q x+y = p+q x+y - q y d y d x p x+p y-p x-q x x(x+y) = p y+q y-q x-q y y(x+y) d y d x (p y-q x) x = (p y-q x) y d y d x d y d x = y x

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