Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202615 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ⁻¹ 1 + 2x 1 - 2x , then d y d x at x = 6 is

Options

  1. A0
  2. B1
  3. C1 2
  4. D3 2

Correct answer

B. 1

Step-by-step solution

We have y = ⁻¹ 1 + 2x 1 - 2x . Using the trigonometric identities 1 + 2x = ( x + x)^2 and 1 - 2x = ( x - x)^2 , we get: y = ⁻¹ ( x + x)^2 ( x - x)^2 = ⁻¹ | x + x x - x | At x = 6 , 6 = 3 2 and 6 = 1 2 . Since x > x , the expression inside the modulus is positive. y = ⁻¹ ( x + x x - x ) Dividing the numerator and the denominator by x : y = ⁻¹ ( 1 + x 1 - x ) y = ⁻¹ ( ( 4 + x ) ) For x = 6 , 4 + x = 5 12 , which lies in the principal branch ( - 2 , 2 ) . y = 4 + x Differentiating with respect to x : d y d x = 1 Answe

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