`x^(3) + x^(2)y+ xy^(2) + y^(3) = 81`

Explanation

To find \(\frac{dy}{dx}\) for the equation \(x^3 + x^2y + xy^2 + y^3 = 81\), we will differentiate both sides of the equation with respect to \(x\) using implicit differentiation. Here’s a step-by-step solution:

### Step 1: Differentiate both sides
We start with the equation:
\[ x^3 + x^2y + xy^2 + y^3 = 81 \]
Differentiating both sides with respect to \(x\):
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