Question

If $ f(x) = \sin^{-1}(2x\sqrt{1 - x^2}) $, then $ f'(x) $ is:

• A. \( \frac{2(1 - 2x^2)}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• B. \( \frac{2x(1 - 2x^2)}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• C. \( \frac{1 - 2x^2}{\sqrt{1 - 4x^2(1 - x^2)}} \)
• D. \( \frac{2x\sqrt{1 - x^2}}{1 - x^2} \)

Hint:

Key Fact: The derivative of \( \sin^{-1}(u) \) is \( \frac{1}{\sqrt{1 - u^2}} \cdot \frac{du}{dx} \).