Find dy dx if x3 + x2y + xy2 + y3 = 81. - Vidyadip

Question

Find $\frac{{dy}}{{dx}}$ if x³ + x²y + xy² + y³ = 81.

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Answer

we have,

x³ + x²y + xy² + y³ = 81

Differentiating both sides w.r.t to x,we get,

$3{x^2} + {x^2}.\frac{{dy}}{{dx}} + y.2x + x.2y\frac{{dy}}{{dx}} + {y^2}.1 + 3{y^2}\frac{{dy}}{{dx}} = 0$

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

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

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