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AP EAMCET202420 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If y=x-x^2 , then the rate of change of y^2 with respect to x^2 at x=2 is

Options

  1. A0
  2. B-1
  3. C3
  4. D9

Correct answer

C. 3

Step-by-step solution

y=x-x^2 Let v=y^2=x^2+x^4-2 x^3 d (y^2 ) d x =2 x+4 x^3-6 x^2u=x^2 d u d x =2 x d v d u = d v / d x d u / d x =1+2 x^2- .3 x d (y^2 ) d (x^2 ) |_ x=2 =1+8-6=3

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