Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202613 April 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ⁻¹ 1 + x^2 - 1 - x^2 1 + x^2 + 1 - x^2 , where |x| < 1 , then dy dx is equal to

Options

  1. A-x 1 - x^4
  2. Bx 1 - x^4
  3. C-2x 1 - x^4
  4. D2x 1 - x^4

Correct answer

B. x 1 - x^4

Step-by-step solution

Let x^2 = 2 . Then = 1 2 ⁻¹(x^2) . Substituting this into the given expression, we get: 1 + x^2 = 1 + 2 = 2 ^2 = 2 1 - x^2 = 1 - 2 = 2 ^2 = 2 Now, substitute these into y : y = ⁻¹ 2 - 2 2 + 2 Dividing the numerator and the denominator by 2 : y = ⁻¹ 1 - 1 + y = ⁻¹ ( 4 - ) y = 4 - Substituting back = 1 2 ⁻¹(x^2) : y = 4 - 1 2 ⁻¹(x^2) Differentiating with respect to x : dy dx = 0 - 1 2 ( -1 1 - (x^2)^2 ) d dx (x^2) dy dx = 1 2 1 1 - x^4 2x dy dx = x 1 - x^4 Answer: x 1 - x^4

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All MHT CET PYQs