Question

find dy/dx


x³+x²y+xy²+y³=81
























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some thanks please

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Answer 1

x³ + x²y + xy² + y³ = 81

See attached picture

Answer 2

$\rm\implies {x}^{3} + {x}^{2} y + {xy}^{2} + {y}^{2} = 81$

$\rm\implies 3 {x}^{2} + ( {y}^{2} x {x}^{2} \frac{dy}{dx} ) + ( {y}^{2} + x. \frac{2ydy}{dx} ) + 3 {y}^{2} \frac{dy}{dx} ≠ 0$

$\rm\implies \frac{dy}{dx} ( {x}^{2} + 2xy + {y}^{2} ) = - {3x}^{2} - 2xy - {y}^{2}$

$\rm\implies \frac{dy}{dx} = \frac{ - 3x^{2} - 2xy - {y}^{2} }{ {x}^{2} + 2xy + 3 {y}^{2} }$

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Hope this will help you!! :)