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MHT CET202411 May 2024Evening ShiftMathematicsDifferentiationActual

If y=( x)^ x , then d y ~d x is equal to

Options

  1. A( x)^ x (1+ ^2 x ( x) )
  2. Bx( x)^ x-1 x
  3. C( x)^ x ^2 x x
  4. Dx( x)^ x-1

Correct answer

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

Step-by-step solution

y=( x)^ x Taking logarithm on both sides, we get y= x ( x) Differentiating w.r.t. x , we get aligned & 1 y ~d y ~d x = x x+ ( x) ^2 x & ~d y ~d x =( x)^ x [1+ ^2 x ( x) ] aligned

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