Derivative of tan⁻¹((√x + √a) / (1 − √(ax))) with respect to x is:

Derivative of tan⁻¹((√x + √a) / (1 − √(ax))) with respect to x is:

• A. 1 / (2√x (1 + x))
• B. 1 / (1 + x)
• C. 1 / (2√x (1 + a))
• D. 0

Answer: A) 1 / (2√x (1 + x))

Explanation: Using the formula tan⁻¹((A + B)/(1 − AB)) = tan⁻¹A + tan⁻¹B. Let A = √x, B = √a. y = tan⁻¹(√x) + tan⁻¹(√a). dy/dx = (1 / (1 + (√x)²)) × (1 / 2√x) = 1 / (2√x(1 + x)).