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COMEDK2013MathematicsInverse Trigonometric Functions

If y= ⁻¹( x- x) , then d y d x is equal to

Options

  1. A2
  2. B-2
  3. C1 2
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

We have, y= ⁻¹( x- x)y= ⁻¹ [ 1- x x ] aligned &= ⁻¹ [ 1- ( 2 -x ) ( 2 -x ) ] &= ⁻¹ [ 2 ² ( 4 - x 2 ) 2 ( 4 - x 2 ) ( 4 - x 2 ) ] &= ⁻¹ ( 4 - x 2 ) = 4 - x 2 d y d x &=- 1 2 aligned

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