Cho hàm số .y=f(x)=x/ căn (4-x^2) Tính y'(0) bằng

* Hướng dẫn giải

Chọn A

$\begin{array}{l}y\text{'}=\frac{1.\sqrt{4-x^2}-x.\frac{(4-x^2)\text{'}}{2\sqrt{4-x{}^2}}}{4-x^2}\\ =\frac{\sqrt{4-x^2}-\frac{x.(-2x)}{2\sqrt{4-x^2}}}{4-x^2}\\ =\frac{\sqrt{4-x^2}\text{}+\frac{x^2}{\sqrt{4-x^2}}}{4-x^2}\end{array}$

$\Rightarrow y\text{'}\left(0\right)=\frac{2+\text{}0}{4-0}=\frac{1}{2}$