Differentiate implicitly to find $\frac{d y}{d x}$. Then find the slope of the curve at the given point. \[ 4 x^{2}-5 y^{3}=-284 \] \[ \frac{d y}{d x}= \]

Step 1 ：Given the equation \(4x^{2}-5y^{3}=-284\), we need to differentiate it implicitly with respect to \(x\).

Step 2 ：Differentiating both sides of the equation with respect to \(x\) gives \(8x - 15y^{2} \frac{dy}{dx} = 0\).

Step 3 ：Rearranging the equation to solve for \(\frac{dy}{dx}\) gives \(\frac{dy}{dx} = \frac{8x}{15y^{2}}\).

Step 4 ：To find the slope of the curve at a given point, we substitute the \(x\) and \(y\) coordinates of the point into the derivative.

Step 5 ：Without a specific point given, we cannot calculate a numerical value for the slope. However, the derivative \(\frac{dy}{dx} = \frac{8x}{15y^{2}}\) gives us the slope of the curve at any point \((x, y)\) on the curve.