You have the following function:
[tex]y=3e^y+x[/tex]Derivate implictly the previous expression, as follow:
[tex]y^{\prime}=3e^yy^{\prime}+1[/tex]Where you have used that:
[tex](e^y)^{\prime}=e^yy^{\prime}[/tex]Then, the implicit derivative of the given expression is:
[tex]y^{\prime}=3e^yy^{\prime}+1[/tex]Next, solve for y' as follow:
[tex]\begin{gathered} y^{\prime}-3e^yy^{\prime}=1 \\ (1-3e^y)y^{\prime}=1 \\ y^{\prime}=\frac{1}{1-3e^y} \end{gathered}[/tex]
