Mind checking my solution anyone? I worry that I may have left out a step because the given coordinates include both x and y values.
Your derivative is incorrect. If $\displaystyle \displaystyle \begin{align*} y = \frac{x^4 + 3}{6x} \end{align*}$, this simplifies to $\displaystyle \displaystyle \begin{align*} y = \frac{1}{6}x^3 + \frac{1}{2}x^{-1} \end{align*}$, not $\displaystyle \displaystyle \begin{align*} \frac{1}{6x^3} + \frac{1}{2}x^{-1} \end{align*}$...