Question:
Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ in each of the following:
$\left(x^{2}+y^{2}\right)^{2}=x y$
Solution:
$2\left(x^{2}+y^{2}\right)\left[2 x+2 y \frac{d y}{d x}\right]=y(1)+x \frac{d y}{d x}$
$\frac{d y}{d x}\left[4 y\left(x^{2}+y^{2}\right)-x\right]=y-4 x\left(x^{2}+y^{2}\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}-4 \mathrm{x}\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)}{4 \mathrm{y}\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)-\mathrm{x}}$
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