Use a graphing calculator to find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation $y^{5}-x y-x^{5}=-12$, where $x=1$

Step 1 ：First, we need to find the derivative of the given equation. The derivative of \(y^{5}-x y-x^{5}\) with respect to \(x\) is \(5y^{4}y'-y-y^{4}-5x^{4}\) by using the chain rule and product rule.

Step 2 ：Next, we substitute \(x=1\) into the original equation to find the corresponding \(y\) value. Substituting \(x=1\) into \(y^{5}-x y-x^{5}=-12\), we get \(y^{5}-y-1^{5}=-12\), which simplifies to \(y^{5}-y-1=-12\). Solving this equation for \(y\), we get \(y^{5}-y+13=0\). This equation has no real roots, so there are no points on the graph where \(x=1\).

Step 3 ：Since there are no points on the graph where \(x=1\), there are no tangent lines at these points.