Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202519 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The derivative of ⁻¹ ( 1+x^2 -1 ) is

Options

  1. Ax 1+x^2 (x^2-2 x+1 +1 )
  2. Bx 1+x^2 (x^2-2 1+x^2 +3 )
  3. Cx 1+x^2 (x^2-2 x^2+1 +2 )
  4. Dx 1+x^2 (x^2+2 1+x^2 -3 )

Correct answer

B. x 1+x^2 (x^2-2 1+x^2 +3 )

Step-by-step solution

Derivative of ( d d x [ ⁻¹ ( 1+x^2 -1 ) ] ) Let (u= 1+x^2 -1 . ) Then ( d d x ⁻¹(u)= u^ 1+u^2 ) We have (u^ = x 1+x^2 ) and (1+u^2=1+ ( 1+x^2 -1 )^2=x^2+3-2 1+x^2 . ) Thus the derivative equals ( x 1+x^2 (x^2-2 1+x^2 +3 ) )

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