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AP EAMCET202022 Sep 2020Morning ShiftMathematicsDifferentiationActual

If y= e^x x x^2 , then d y d x =

Options

  1. Ae^x 1+(x+2) x x^3
  2. Be^x 1-(x-2) x x^4
  3. Ce^x 1-(x-2) x x^3
  4. De^x 1+(x-2) x x^3

Correct answer

D. e^x 1+(x-2) x x^3

Step-by-step solution

It is given that, y= e^x x x^2 On applying logarithm both sides, we get _e y=x+ _e( x)-2 x Now, on differentiating both sides w.r.t ' x ', we get aligned 1 y ( d y d x ) & =1+ 1 x x - 2 x d y d x & =y (1+ 1 x x - 2 x ) aligned aligned & = e^x x x^2 ( x x+1-2 x x x ) & = e^x x^3 [1+(x-2) x] aligned Hence, option (4) is correct.

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