The derivative of tan⁻¹(sin x - cos x / sin x + cos x), with respect to x², where x ∈ (0, π/2) is

Correct option is D. 2
Let y = tan⁻¹((sin x - cos x)/(sin x + cos x)) and z = x²
Numerator and denominator divides by cos x ⇒ y = tan⁻¹((tan x - 1)/(tan x + 1)) ⇒ y = tan⁻¹(tan(x - π/4)) ≈ tan(A+B) = (x - π/4) ∈ (-π/4, π/4)
∴ y = x - π/4
differentiate w.r.t. x.
dy/dx = 1
and dz/dx = 2x
Since dy/dz = (dy/dx)/(dz/dx) ⇒ dy/dx = 2
Hence, Option (D) is correct.