If f(x) = eˣ, g(x) = sin⁻¹ x, then derivative of f(g(x)) at x = 1/2 is:

If f(x) = eˣ, g(x) = sin⁻¹ x, then derivative of f(g(x)) at x = 1/2 is:

• A. e^(π/6) × 2/√3
• B. e^(π/6) × √3
• C. e^(1/2) × 2/√3
• D. e^(sin⁻¹ x)

Answer: A) e^(π/6) × 2/√3

Explanation: f(g(x)) = e^(sin⁻¹ x). Derivative = e^(sin⁻¹ x) × 1/√(1−x²). At x=1/2, sin⁻¹(1/2) = π/6, 1/√(1−1/4) = 2/√3. So value is e^(π/6) × 2/√3.