[tex]\bf x^3=ln(xy)\implies x^3=ln(x)+ln(y)
\\\\\\
3x^2=\cfrac{1}{x}+\stackrel{chain~rule}{\cfrac{1}{y}\cdot \cfrac{dy}{dx}}\implies 3x^2-\cfrac{1}{x}=\cfrac{\frac{dy}{dx}}{y}
\\\\\\
\left. y\left( 3x^2-\frac{1}{x} \right)=\cfrac{dy}{dx} \right|_{1,e}\implies e\left[ 3(1)^2-\frac{1}{1} \right]\implies 2e[/tex]
