COMEDK202510 May 2025Morning ShiftMathematicsDifferentiationActual
If y= ⁻¹ ( 1 x+1 ) then d y d x =
Options
- A1 2 x(1+ x )
- B- 1 2 x (1+x)
- C1 2 1-x
- D1 2 x (1+ x )
Correct answer
B. - 1 2 x (1+x)
Step-by-step solution
Given y = ⁻¹ ( 1 x+1 ) . Let u = 1 x+1 . Then y = ⁻¹(u) . Using the chain rule, dy dx = dy du du dx . dy du = 1 1-u^2 = 1 1 - 1 x+1 = 1 x+1-1 x+1 = x+1 x = x+1 x . Now, u = (x+1)^ -1/2 . du dx = - 1 2 (x+1)^ -3/2 = - 1 2(x+1) x+1 . Multiplying these results: dy dx = x+1 x (- 1 2(x+1) x+1 ) = - 1 2 x (x+1) . Answer: - 1 2 x (1+x)