Question

${x}^{y} = {y}^{x} find \: {dy} \div dx$
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Answer 1

$y^x=x^y\\\\\\y=\left(x^y\right)^{\frac{1}{x}}\\\\\\y=x^{\frac {y}{x}}\\\\\\\dfrac {dy}{dx}=\dfrac {y}{x}\ x^{\frac {y}{x}-1}\\\\\\\dfrac {dy}{dx}=x^{\frac {y}{x}-2}\ y\\\\\\\underline {\underline {\dfrac {dy}{dx}=x^{\frac {y-2x}{x}}\ y}}$