Cho hàm số y=f(x)=sin cănx+cos cănx Giá trị bằng:

* Hướng dẫn giải

Đáp án A

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