Differentiate implicitly to find $\frac{d y}{d x}$. Then find the slope of the curve at the given point. \[ y^{2}-x^{3}=28 ; \quad(2,-6) \] \[ \frac{d y}{d x}= \]

Step 1 ：Differentiate both sides of the equation \(y^{2}-x^{3}=28\) with respect to x. For the left side, use the chain rule to differentiate \(y^2\), and for the right side, use the power rule to differentiate \(x^3\).

Step 2 ：The derivative of the equation is \(-3x^2\). However, this is not the final derivative as we have not taken into account the derivative of y with respect to x. We need to apply the chain rule to the term \(y^2\) in the equation.

Step 3 ：The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is \(y^2\) and the inner function is y. The derivative of y with respect to x is \(dy/dx\). Therefore, we need to add \(2y*dy/dx\) to the derivative.

Step 4 ：Solve the equation for \(dy/dx\) to find the derivative of y with respect to x. The derivative of y with respect to x is \(\frac{3x^2}{2y}\).

Step 5 ：Substitute the given point into the derivative to find the slope of the curve at that point. The slope of the curve at the point (2,-6) is -1.

Step 6 ：Final Answer: The derivative of y with respect to x is \(\frac{3x^2}{2y}\). The slope of the curve at the point (2,-6) is \(\boxed{-1}\).