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MHT CET202121 Sep 2021Morning ShiftMathematicsDifferentiationActual

If e^ -y y=x , then d y d x is

Options

  1. Ay 1-y
  2. B1 x y(1-y)
  3. C1 x(1-y)
  4. Dy x (1- y )

Correct answer

D. y x (1- y )

Step-by-step solution

aligned & e^ -y y=x & y e^y =x y=x e^y aligned and e ^ y = y x Now y= xe ^ y aligned & d y d x =x e^y d y d x +e^y & d y d x (x e^y-1 )=-e^y d y d x = -e^y x e^y-1 aligned From (1) and (2), we write d y d x =- ( y x ) 1 y-1 = -y x(y-1) = y x(1-y)

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