Step 1: Write out the expression
[tex]2x^3+3y^2=7xy[/tex]Step 2: Differentiate implicitly
[tex]\begin{gathered} 6x^2+6yy^{\prime}=7(xy^{\prime}+y) \\ \text{ Wh}ere \\ y^{\prime}=\frac{\text{ dy}}{dx} \end{gathered}[/tex]Step 4: Isolate y'
[tex]\begin{gathered} 6x^2+6yy^{\prime}=7xy^{\prime}+7y \\ 6yy^{\prime}-7xy^{\prime}=7y-6x^2 \\ y^{\prime}(6y-7x)=7y-6x^2 \\ \text{Dividing both sides by }6y-7x,\text{ we have} \end{gathered}[/tex][tex]y^{\prime}=\frac{7y-6x^2}{6y-7x}[/tex]Hence the derivative is
[tex]\frac{7y-6x^2}{6y-7x}[/tex](7y - 6x²)/(6y - 7x)
