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AP EAMCET202017 Sep 2020Morning ShiftMathematicsDifferentiationActual

If (x²⁰¹⁹ y²⁰²⁰=(x+y)⁴⁰³⁹ ), then ( d y d x = )

Options

  1. A0
  2. B( x y )
  3. C( y x )
  4. D1

Correct answer

C. ( y x )

Step-by-step solution

(x²⁰¹⁹ y²⁰²⁰=(x+y)⁴⁰³⁹ ) On differentiating ( gathered 2020 y²⁰¹⁹ d y d x x²⁰¹⁹+2019 x²⁰¹⁸ y²⁰²⁰ =4039(x+y)⁴⁰³⁸ (1+ d y d x ) 2020 (x+y)⁴⁰³⁹ y d y d x +2019 (x+y)⁴⁰³⁹ x =4039(x+y)⁴⁰³⁸ (1+ d y d x ) ( 2020 y d y d x + 2019 x )(x+y)=4039 (1+ d y d x ) 2020(x+y) y d y d x + 2019 x (x+y)=4039 (1+ d y d x ) d y d x [4039- 2020(x+y) y ]= 2019(x+y) x d y d x [ 2019 y-2020 x y ]= 2019(x+y) x -4039 d y d x = y x gathered )

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