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MHT CET202521 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ^2 ( ⁻¹ ( 1-x 1+x ) ) , then dy d x =

Options

  1. A-1
  2. B1
  3. C- 1 4
  4. D1 2

Correct answer

D. 1 2

Step-by-step solution

To find the derivative of y = ^2 ( ⁻¹ ( 1-x 1+x ) ) , simplify the expression through trigonometric substitution. Let x = . With [0, ) , it follows that 1- 1+ = ( /2) . Then ⁻¹( ( /2)) = ⁻¹( ( /2 - /2)) = /2 - /2 , so y = ^2( /2 - /2) = ^2( /2) . Since ^2( /2) = 1 + 2 and x = , we have y = 1 + x 2 . Differentiating gives dy dx = 1 2 . Final Answer: 1 2

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