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MHT CET202121 Sep 2021Morning ShiftMathematicsDifferentiationActual

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

Options

  1. A( x)^x [ 1 x ( x) ]
  2. B( )^x [ x+ 1 ( x) ]
  3. Cx( )^x [ 1 x + ( x) ]
  4. Dx( )^x [ x+ 1 ( x) ]

Correct answer

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

Step-by-step solution

Let u =( x )^ x aligned & u = x [ ( x )^ x ] & 1 u du dx = x ( x ) 1 x + ( x )= ( x )+ 1 x & du dx =( x )^ x [ 1 x + ( x ) ] aligned Let v= x d v d x = 1 x d u d v =( x)^x(x) [ 1 x + ( x) ]

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