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MHT CET20255 May 2025Evening ShiftMathematicsDifferentiationActual

If x _ e ( _ e x )-x^2+ y ^2=4( y >0) , then dy d x at x= e is

Options

  1. Ae 4+ e ^2
  2. B2 e-1 2 4+e^2
  3. C1+2 e 4+ e ^2
  4. D1+2 e 2 4+e^2

Correct answer

B. 2 e-1 2 4+e^2

Step-by-step solution

To find the derivative at x = e , first determine the corresponding y -value from x _e( _e x) - x^2 + y^2 = 4 . Substituting x = e gives e _e(1) - e^2 + y^2 = 4 . Since _e(1) = 0 , this simplifies to -e^2 + y^2 = 4 . Solving for y with the condition y > 0 yields y = 4 + e^2 . Differentiating the equation implicitly with respect to x results in d dx (x _e( _e x)) - d dx (x^2) + d dx (y^2) = d dx (4) . Applying the product rule to the first term gives 1 _e( _e x) + x 1 x _e x = _e( _e x) + 1 _e x . The second term is

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