Find the equation of the tangent line at the given value of x on the curve.
2xy - 2x + y = - 14 , x = 2
rearaning and facotring we get $\displaystyle y(2x+1)-2x=-14\Rightarrow{y=\frac{2x-14}{2x+1}}$ so $\displaystyle y'=\frac{2}{2x+1}-\frac{2(2x-14)}{(2x+1)^2}$ so now use the equation of the tangetn line $\displaystyle y-f(x_0)=f'(x_0)(x-x_0)$ to obtain yoru answer