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MHT CET2010MathematicsDifferentiation

The derivative of ( x)^ x with respect to x is

Options

  1. A( x)^ x [ 1 x + ( x) ]
  2. B( x)^ x [ x+ 1 ( x) ]
  3. Cx( x)^ x [ 1 x + ( x) ]
  4. DNone of the above

Correct answer

C. x( x)^ x [ 1 x + ( x) ]

Step-by-step solution

Let u=( x)^ x array ll & u=x ( x) & 1 u d u d x =x 1 x 1 x + ( x) & d u d x =( x)^ x [ 1 x + ( x) ] array and v= x d v d x = 1 x Now, d u d v =( x)^ x [ 1 x ( x) ] x=x( x)^ x [ 1 x + ( x) ]

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