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COMEDK2024MathematicsDifferentiationActual

If y= ⁻¹( x ) , then d y d x equals

Options

  1. A1 2 1+ cosec x
  2. B1 2 1- x
  3. C1 2 1- cosec x
  4. D1 2 1+ x

Correct answer

A. 1 2 1+ cosec x

Step-by-step solution

dy dx = 1 1 - x x 2 x = x 2 x(1 - x) Using ^2 x = 1 - ^2 x = (1 - x)(1 + x) : dy dx = 1 2 ^2 x x(1- x) = 1 2 (1- x)(1+ x) x(1- x) = 1 2 1+ x x = 1 2 cosec x + 1 = 1 2 1 + cosec x

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