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AP EAMCET202018 Sep 2020Evening ShiftMathematicsDifferentiationActual

The derivative of (f(x)= ⁻¹ [ 1+x 2 ]+x^x ) with respect to (x ) at (x=1 ) is equal to

Options

  1. A1
  2. B( 1 4 )
  3. C( 3 4 )
  4. D( 2 3 )

Correct answer

C. ( 3 4 )

Step-by-step solution

Given, ( aligned f(x) & = ⁻¹ ( 1+x 2 )+x^x & = 2 - ⁻¹ ( 1+x 2 )+x^x & = 2 - 1+x 2 +x^x aligned ) ( f^ (x)= -1 2 1 2 1+x +x^x ( _e(e x) ) ) ( [ d (x^x ) d x =x^x _e(e x) ] ) On putting (x=1 ), we get (f^ (1)= -1 4 +1= 3 4 ) Hence, option (c) is correct.

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