求定积分$\int_{0}^{1}\dfrac{x}{\sqrt{1 + x^{2}}}dx$.

求参数方程$\begin{cases}x=\dfrac{1}{2}\cos^{3}t\\y=\dfrac{1}{2}\sin^{3}t\end{cases}$的导数$\dfrac{dy}{dx}$.

已知$y = \arctan\sqrt{x}$，求$\dfrac{dy}{dx}$及$\dfrac{dy}{dx}\vert_{x = 1}$.