Cho hàm số

Câu hỏi: Cho hàm số $y={\left(\sin x\right)}^{\sqrt{\cos x}}$ ta có

A. $y\text{'}\left(\frac{\mathrm{\pi }}{4}\right)=e^{\frac{1}{2\sqrt[4]{2}}\ln 2}\left(\frac{1}{\sqrt[4]{2}}+\frac{1}{4\sqrt[4]{2}}\ln 2\right)$

B. $y\text{'}\left(\frac{\mathrm{\pi }}{4}\right)=e^{\frac{1}{2\sqrt[4]{2}}\ln 2}\left(\frac{1}{\sqrt{2}}+\frac{1}{4\sqrt{2}}\ln 2\right)$

C. $y\text{'}\left(\frac{\mathrm{\pi }}{4}\right)=e^{\frac{1}{2\sqrt[4]{2}}\ln 2}\left(\frac{1}{\sqrt[4]{2}}-\frac{1}{4\sqrt[4]{2}}\ln 2\right)$

D. $y\text{'}\left(\frac{\mathrm{\pi }}{4}\right)=e^{\frac{1}{2\sqrt[4]{2}}\ln 2}\left(\frac{1}{\sqrt{2}}-\frac{1}{4\sqrt{2}}\ln 2\right)$