\documentclass[12pt]{exam}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
%% Use \begin{solution} \end{solution} to write solutions.
\date{}
\begin{document}
\title{Assignment 5} %Replace X by HW number or to any other title%
\maketitle
\begin{questions}
\question % Enter the 1st question
%% Add another \question if you want to put more than one questions in one page.
Consider the curve $2x^3y+xy^2=8$. Determine the equation of the tangent line to the curve at the point $(1,2)$ . Find $y''.$
\pagebreak
\question % Enter the 2nd question
Consider the curve $x^5y+2xy^2=10$. Determine the equation of the tangent line to the curve at the point $(1,2)$ . Find $y''.$
\pagebreak
\question Find $y'$ if $x^2+y^2+2xy=0.$
\pagebreak
\question % Enter the 4th question
Consider the curve given by the equation $-xy+lny=1.$ Find an expression for $dy/dx$ and use it to find the equation of the tangent line at $(-1,1).$
\pagebreak
\question % Enter the 5th question
Suppose $y$ is a function of $x$ defined implicitly by the equation $x+16=y^x.$ Use implicit differentiation to find $y'(x)$ and $y''(x).$
\pagebreak
%\question % Enter the 6th question
\end{questions}
\end{document}