求曲线$y = \tan x+ 2e^{x}$在点$(0,2)$处的法线方程.

已知方程$y = xy^{3}+e^{x}$所确定的函数为$y = y(x)$，求$dy$.

设参数方程为$\begin{cases}x = 1+\sin2\theta\\y = 2\sin\theta + 3\end{cases}$，$\theta$为参数，求$\left.\dfrac{dy}{dx}\right|_{\theta = 0}$.