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NDA2022MathematicsDifferentiationActual

If y= (x^ x )^ x then which one of the following is correct?

Options

  1. Ad y d x +x y(1+2 x)=0
  2. Bd y d x -x y(1+2 x)=0
  3. Cd y d x -2 x y(1+2 x)=0
  4. Dd y d x -2 x y(1+2 x)=0

Correct answer

B. d y d x -x y(1+2 x)=0

Step-by-step solution

y= (x^x )^x=x^ x^2 Taking both sides, we get y=x^2 x Differentiate w.r.t to x . 1 y d y d x =2 x x+x^2 1 x aligned & d y d x =(x+2 x x) d y d x =x y(1+2 x) & d y d x -x y(1+2 x)=0 aligned

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