Cho hàm số f(x)=sin căn x + cos căn x . Giá trị bằng

* Hướng dẫn giải

Chọn A

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

$\begin{array}{l}f\text{'}\left(\frac{{\pi }^2}{16}\right)=\frac{1}{2\sqrt{{\left(\frac{\pi }{4}\right)}^2}}\left(\cos \sqrt{{\left(\frac{\pi }{4}\right)}^2}-\sin \sqrt{{\left(\frac{\pi }{4}\right)}^2}\right)\\ =\frac{1}{2.\frac{\pi }{4}}\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\right)=0\end{array}$