已知函数 f(t)=∫1tdx∫x1sinxydy,则 f′(π2)\text{已知函数 }f(t)=\int_{1}^{t}dx\int_{\sqrt{x}}^{1}\sin\frac{x}{y}dy,\text{则 }f^{\prime}\left(\frac{\pi}{2}\right)______.
π∫π2π2cosuu3du−cosπ22−π2cosπ2.\pi\int_{\sqrt{\frac{\pi}{2}}}^{\frac{\pi}{2}}\frac{\cos u}{u^3}du-\frac{\cos\sqrt{\frac{\pi}{2}}}{2}-\sqrt{\frac{\pi}{2}}\cos\sqrt{\frac{\pi}{2}}.
2