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MHT CET202618 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

For x > 0 and (x x) < 1 , if y = ⁻¹ ( x - x^ x^2 e^ x^2 + x^x ) , then dy dx =

Options

  1. A1 1+x^2 + 2 x[1+( x)^2]
  2. B1 1+x^2 + 1 x[1+( x)^2]
  3. C-1 1+x^2 + 1 x[1+( x)^2]
  4. D1 1+x^2 + 1 [1+( x)^2]

Correct answer

B. 1 1+x^2 + 1 x[1+( x)^2]

Step-by-step solution

Given function is: y = ⁻¹ ( x - x^ x^2 e^ x^2 + x^x ) Simplify the numerator and the denominator of the argument: Numerator = x - x^2 x = x(1 - x x) Denominator = x^2 e + x x = x^2 + x x = x(x + x) Substitute these back into the function: y = ⁻¹ ( x(1 - x x) x(x + x) ) = ⁻¹ ( 1 - x x x + x ) We know the inverse trigonometric identity ⁻¹ ( 1 - ab a + b ) = ⁻¹ ( a + b 1 - ab ) (up to a constant multiple of depending on the sign of a+b , which becomes zero upon differentiation). Using a = x and b = x , and given x x 0

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