Chọn phương án A.

\(\begin{aligned}
f'(x)&=\dfrac{x'\cdot\sqrt{4-x^2}-x\sqrt{4-x^2}'}{\sqrt{4-x^2}^2}\\
&=\dfrac{\sqrt{4-x^2}-x\cdot\dfrac{\left(4-x^2\right)'}{2\sqrt{4-x^2}}}{4-x^2}\\
&=\dfrac{\sqrt{4-x^2}-\dfrac{x\left(-2x\right)}{2\sqrt{4-x^2}}}{4-x^2}\\
&=\dfrac{\sqrt{4-x^2}+\dfrac{x^2}{\sqrt{4-x^2}}}{4-x^2}\\
&=\dfrac{\left(4-x^2\right)+x^2}{\left(4-x^2\right)\sqrt{4-x^2}}\\
&=\dfrac{4}{\left(4-x^2\right)\sqrt{4-x^2}}.
\end{aligned}\)

Khi đó \(f'(0)=\dfrac{4}{\left(4-0^2\right)\sqrt{4-0^2}}=\dfrac{1}{2}\).