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MHT CET202124 Sep 2021Morning ShiftMathematicsDifferentiationActual

If y=x y , then d y d x =

Options

  1. Ax x-y^2
  2. By x-x^2-y^2
  3. Cx x-x^2-y^2
  4. Dy y-x

Correct answer

B. y x-x^2-y^2

Step-by-step solution

aligned & y=x y & d y d x =x ^2 y d y d x + y & (x ^2 y-1 ) d y d x =- y & d y d x = - y x ^2 y-1 = -x y x^2 ^2 y-x & = -x y x^2 (1+ ^2 y )-x = -x y x^2+x^2 ^2 y-x & d y d x = -y x^2+y^2-x = y x-x^2-y^2 [ y=x y, given ] aligned

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