Evaluate the derivative of the following function at the given point. \[ 18 x^{3} y^{2}-6 y^{3}=1,458 ;(2,-3) \] \[ \left.\frac{d y}{d x}\right|_{(2,-3)}= \]

Step 1 ：We are given the function \(18x^{3}y^{2} - 6y^{3} = 1458\) and we are asked to find the derivative of y with respect to x at the point (2,-3).

Step 2 ：We start by differentiating both sides of the equation with respect to x. The derivative of \(18x^{3}y^{2}\) with respect to x is \(54x^{2}y^{2} + 36x^{3}y\frac{dy}{dx}\) by using the product rule and chain rule.

Step 3 ：The derivative of \(-6y^{3}\) with respect to x is \(-18y^{2}\frac{dy}{dx}\) by using the chain rule.

Step 4 ：Setting the derivative of the left-hand side equal to the derivative of the right-hand side (which is 0 because the right-hand side is a constant), we can solve for \(\frac{dy}{dx}\).

Step 5 ：After finding the general form of \(\frac{dy}{dx}\), we can substitute the given point (2,-3) into the equation to find the specific value of \(\frac{dy}{dx}\) at that point.

Step 6 ：The derivative of the function at the point (2,-3) is \(\boxed{1944}\).