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JEE Main2006MathematicsDifferentiationActual

If x^m y^n=(x+y)^ m+n , then d y d x is

Options

  1. Ay x
  2. Bx+y x y
  3. Cxy
  4. Dx y

Correct answer

A. y x

Step-by-step solution

x^m y^n=(x+y)^ m+n m x+n y=(m+n) (x+y) m x + n y d y d x = m+n x+y (1+ d y d x ) ( m x - m+n x+y )= ( m+n x+y - n y ) d y d x m y-n x x(x+y) = ( m y-n x y(x+y) ) d y d x d y d x = y x

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