Find `(dy)/(dx)` in the following:
(a)`x^3+x^2y+x y^2+y^3=81`
(b) `xy+y^2 =tan x+ y `
(c) `x^2 + xy+ y^2 = 100`

Explanation

Let's solve the given problems step by step.

### Part (a): Find \(\frac{dy}{dx}\) for the equation \(x^3 + x^2y + xy^2 + y^3 = 81\).

1. **Differentiate both sides with respect to \(x\)**:
\[ \frac{d}{dx}(x^3) + \frac{d}{dx}(x^2y) + \frac{d}{dx}(xy^2) + \frac{d}{dx}(y^3) = \frac{d}{dx}(81) \]
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