Question $4$: Given the curve defined by: $x{y}^2=2e^x-2y.$

a$)$ Find $\frac{dy}{dx},$ Show your work. $(5$ pts$)$

b$)$ Use the answer in part a$)$ to find the equation of the tangent line to the above curve at the point $(0,1).(5$ pts$)$

Question $5$: Use the tangent line to the graph of $y=tan(2x)$ at $z=\frac{}{6}$ to approaimate $tan(\frac{7}{7}).$ Show your work. $($i$0$ pts$)$

Question $6$: Find the derivative of $f(x)=\sqrt[\phantom{2}]{1ln(2lo{n}^2)}$ using the chain rule. Show your work. $(10$ pes$)$