#### Answer

\[{y^,} = \frac{{6x\ln x - 3x}}{{\,{{\left( {\ln x} \right)}^2}}}\]

#### Work Step by Step

\[\begin{gathered}
y = \frac{{3{x^2}}}{{\ln x}} \hfill \\
Differentiate \hfill \\
{y^,} = \,\,{\left[ {\frac{{3{x^2}}}{{\ln x}}} \right]^,} \hfill \\
Use\,\,the\,\,quotient\,\,rule \hfill \\
{y^,} = \frac{{\,\left( {\ln x} \right)\,{{\left( {3{x^2}} \right)}^,} - \,\left( {3{x^2}} \right)\,{{\left( {\ln x} \right)}^,}}}{{\,{{\left( {\ln x} \right)}^2}}} \hfill \\
Where\,\,\,\,{\left[ {\ln x} \right]^,} = \frac{1}{x}\,\,,\,\,Then \hfill \\
{y^,} = \frac{{\,\left( {\ln x} \right)\,\left( {6x} \right) - 3{x^2}\,\left( {\frac{1}{x}} \right)}}{{\,{{\left( {\ln x} \right)}^2}}} \hfill \\
Multiplying \hfill \\
{y^,} = \frac{{6x\ln x - 3x}}{{\,{{\left( {\ln x} \right)}^2}}} \hfill \\
\end{gathered} \]