Cho hàm số

C

- Hướng dẫn giải

Chọn C

$\begin{array}{l}y=\frac{1}{\sqrt{\sin x}}\\ \Rightarrow y^2=\frac{1}{\sin x}\\ \Rightarrow y\text{'}2y=\frac{-\cos x}{{\sin }^{2}x}\end{array}$

$\begin{array}{l}\Rightarrow y\text{'}=\frac{1}{2y}.\left(\frac{-\cos x}{{\sin }^{2}x}\right)\\ =\frac{1}{\frac{2}{\sqrt{\sin x}}}\left(\frac{-\cos x}{{\sin }^{2}x}\right)\\ =\frac{-\sqrt{\sin x}}{2}.\frac{\cos x}{{\sin }^{2}x}\end{array}$

$\begin{array}{l}f\text{'}\left(\frac{\pi }{2}\right)=\frac{-\sqrt{\sin \left(\frac{\pi }{2}\right)}}{2}.\frac{\cos \left(\frac{\pi }{2}\right)}{{\sin }^2\left(\frac{\pi }{2}\right)}\\ =\frac{-1}{2}.\frac{0}{1}=0\end{array}$