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AP EAMCET202315 May 2023Evening ShiftMathematicsDifferentiationActual

If x^x y^y=e^e , then ( d^2 y d x^2 )_ (e, e) =

Options

  1. A1 e ( d y d x )_ (e, e)
  2. B( dy dx )_ ( e , e ) + 1 e
  3. C( d y d x )_ (e, e) - 1 e
  4. De ( d y d x )_ (e, e)

Correct answer

A. 1 e ( d y d x )_ (e, e)

Step-by-step solution

Given x^x y^y=e^e Since (x^x y^y )= (e^e ) x (x)+y (y)=e Differentiating with respect to x . aligned & x x + (x)+ y y y^ + (y) y^ =0 & 1+ (x)+y^ + (y) y^ =0 aligned Again differentiating w.r.t x . 1 x +y^ + (y) y^ + y^ y y^ =0 at ( e , e ) y^ (e)=- 1 e and y^ (e)=-1 So y^ (e)= y^ (e) e

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