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NDA2017MathematicsDifferentiationActual

If y =( x )^ ( x )^ ( x)^ x , then dy dx is equal to

Options

  1. A- y^2 x 1-y In ( x)
  2. By^2 x 1+y In ( x)
  3. Cy^2 x 1-y In ( x )
  4. Dy^2 x 1+y In ( x)

Correct answer

A. - y^2 x 1-y In ( x)

Step-by-step solution

aligned & y=( x)^ ( x)^ x & y=( x)^y aligned y=y x Differentiating on both sides, we get aligned & 1 y d y d x =y(- x)+ x d y d x & d y d x ( 1 y - x )=-y x aligned d y d x = -y x 1 y - x = -y^2 x 1-y x

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