COMEDK2024MathematicsDifferentiationActual
If y= ⁻¹( x ) , then d y d x equals
Options
- A1 2 1+ cosec x
- B1 2 1- x
- C1 2 1- cosec x
- D1 2 1+ x
Correct answer
A. 1 2 1+ cosec x
Step-by-step solution
dy dx = 1 1 - x x 2 x = x 2 x(1 - x) Using ^2 x = 1 - ^2 x = (1 - x)(1 + x) : dy dx = 1 2 ^2 x x(1- x) = 1 2 (1- x)(1+ x) x(1- x) = 1 2 1+ x x = 1 2 cosec x + 1 = 1 2 1 + cosec x