find the equation of the tangent line to the curve:
$\displaystyle xy^3+xy=14 $
At point (7,1).
find $\displaystyle \frac{dy}{dx}$ in terms of $\displaystyle x$ and $\displaystyle y$, then sustitute $\displaystyle 7$ for $\displaystyle x$ and $\displaystyle 1$ for $\displaystyle y$ in the derivative expression to find the slope at that point.