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JEE Main2012MathematicsDifferentiationActual

If f^ (x)= ( x) and y=f ( 2 x+3 3-2 x ) , then d y d x equals

Options

  1. A[ ( 2 x+3 3-2 x ) ]
  2. B12 (3-2 x^2 )
  3. C12 (3-2 x^2 ) [ ( 2 x+3 3-2 x ) ]
  4. D12 (3-2 x^2 . [ ( 2 x+3 3-2 x ) ]

Correct answer

C. 12 (3-2 x^2 ) [ ( 2 x+3 3-2 x ) ]

Step-by-step solution

Let f^ (x)= [ x] and y=f ( 2 x+3 3-2 x ) Now, d y d x =f^ ( 2 x+3 3-2 x ) d d x ( 2 x+3 3-2 x ) aligned & = [ ( 2 x+3 3-2 x ) ] [(6-4 x-)-4 x-6] (3-2 x^2 ) & = 12 (3-2 x^2 . [ ( 2 x+3 3-2 x ) ] aligned

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