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

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Answer

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

Steps

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

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

Step 3 ：Rearranging the equation to solve for $\frac{d y}{d x}$ gives $\frac{d y}{d x} = \frac{8 x}{15 y^{2}}$ .

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 $\frac{d y}{d x} = \frac{8 x}{15 y^{2}}$ gives us the slope of the curve at any point $(x, y)$ on the curve.

Differentiate implicitly to find dydx. Then find the slope of the curve at the given point.4x2−5y3=−284dydx=

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