Question

X^3+y^3=3axy find dy/dx

Answer 1

$x^3+y^3=3axy$
$\dfrac{\mathrm d}{\mathrm dx}\left[x^3+y^3\right]=\dfrac{\mathrm d}{\mathrm dx}[3axy]$
$3x^2+3y^2\dfrac{\mathrm dy}{\mathrm dx}=3a\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$
$\left(3y^2-3ax\right)\dfrac{\mathrm dy}{\mathrm dx}=3ay-3x^2$
$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3ay-3x^2}{3y^2-3ax}$
$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{ay-x^2}{y^2-ax}$