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

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 $2y\ast dy/dx$ 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 $\boxed{{\displaystyle -1}}$.