Use implicit differentiation to find $y^{\prime}$, and then evaluate $y^{\prime}$ for $x^{2} y-3 x^{2}-4=0$ at the point $(2,4)$. \[ \begin{array}{l} y^{\prime}=\square \\ \left.\left.y^{\prime}\right|_{(2,4)}=\square \text { (Simplify your answer. }\right) \end{array} \]

Step 1 ：Differentiate the given equation implicitly with respect to x. This involves applying the product rule to the term \(x^{2} y\) and then differentiating the remaining terms normally. The differentiated equation is \(2xy - 6x\).

Step 2 ：Solve the resulting equation for \(y^{\prime}\) to find the derivative of y with respect to x. The derivative, \(y^{\prime}\), is \(2x(y - 3)\).

Step 3 ：Substitute the coordinates of the given point into the expression for \(y^{\prime}\) to find the value of the derivative at that point. The value of \(y^{\prime}\) at the point \((2,4)\) is \(4\).

Step 4 ：So, the final answer is: \(y^{\prime}=2x(y - 3)\) and \(\boxed{\left.y^{\prime}\right|_{(2,4)}=4}\).