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MHT CET20225 Aug 2022Morning ShiftMathematicsDifferentiationActual

If y= (x^x ) x , then d y d x =

Options

  1. Ax^ x^2 (1+ x)
  2. Bx x^ x^2 (1+ x)
  3. Cx^ x^2 (1+2 x)
  4. Dx x^ x^2 (2 x+1)

Correct answer

D. x x^ x^2 (2 x+1)

Step-by-step solution

y= (x^x ) x y=x x^x=x^2 x Differentiating both sides w.r.t. x aligned & 1 y d y d x =x^2 1 x +2 x x & d y d x =y(x+2 x x) & d y d x = (x^x )^x x(1+2 x) & d y d x =x^ x^2 x(1+2 x) aligned

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