${f}'(x)=\frac{1}{2\sqrt{x}}\times 3{{\sin }^{2}}(\sqrt{x})\cos (\sqrt{x})\times \frac{1}{2\sqrt{{{\sin }^{3}}(\sqrt{x})}}$  ${f}'(\frac{{{\pi }^{2}}}{16})=\frac{1}{2\times \frac{\pi }{4}}\times 3{{\sin }^{2}}(\frac{\pi }{4})\cos (\frac{\pi }{4})\times \frac{1}{2\sqrt{{{\sin }^{3}}(\frac{\pi }{4})}}$  ${f}'(\frac{{{\pi }^{2}}}{16})=\frac{2}{\pi }\times \frac{3}{2}\times \frac{\sqrt{2}}{2}\times \frac{1}{2\sqrt{\frac{\sqrt{2}}{4}}}=\frac{3\sqrt{2}}{2\pi }\times \frac{1}{\sqrt[4]{2}}=\frac{3\sqrt[4]{2}}{2\pi }$