设$y = f(x)$是由方程$e^{xy}+xy+\cos x = 1$确定的隐函数，求$y^{\prime}$.

已知曲线$\begin{cases}y = \sin2t \\ x = \cos t\end{cases}$，求$\left.\dfrac{dy}{dx}\right|_{t = \dfrac{\pi}{4}}$.

计算$\int\dfrac{1}{x^{2}\sqrt{x^{2}+1}}dx$.