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KCET2019MathematicsDifferentiation

If ( f(x)= ⁻¹ [ 2^ x+1 1+4^ x ] ), then ( f^ (0)= )

Options

  1. A( 2 )
  2. B( 4 2 5 )
  3. C( 2 2 )
  4. D( 2 2 5 )

Correct answer

A. ( 2 )

Step-by-step solution

(A) ( f(x)= ⁻¹ [ 2 2^ x 1+ (2^ x )² ] ) Put ( 2 x= ) [ array l f(x)= ⁻¹ [ 2 1+ ( ² ) ] = ⁻¹ 2 f(x)=2 f(x)=2 ⁻¹ (2^ x ) f^ (x)= 2 1+ (2^ x )² 2^ x _ e ² f^ (0)= _ e 2 array ]

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