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AP EAMCET202021 Sep 2020Morning ShiftMathematicsDifferentiationActual

If (y= cosec ⁻¹(x) ) and ( d y d x = -1 |x| x^2-1 ), then

Options

  1. A(y (- 2 , 0 ) )
  2. B(y (- 2 , 2 ) )
  3. C(y (- 2 , 0 ) (0, 2 ) )
  4. D(y R )

Correct answer

C. (y (- 2 , 0 ) (0, 2 ) )

Step-by-step solution

It is given that, (y= cosec ⁻¹ x ) ( and d y d x = -1 |x| x^2-1 ) ( ) Domain of ( cosec ⁻¹ x ) is ( [- 2 , 2 ]- 0 ) and the ( d y d x ) is define for (x (- 2 , 0 ) (0, 2 ) ). Because for derivatives we should exclude the end points of a internal. Hence, option (c) is correct.

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