Answer
\[{y^,} = \frac{3}{2}\,\left( {\frac{{15{x^2} - 2}}{{5{x^3} - 2x}}} \right)\]
Work Step by Step
\[\begin{gathered}
y = \ln \,{\left( {5{x^3} - 2x} \right)^{3/2}} \hfill \\
Use\,\,the\,\,\log \,\,property \hfill \\
\ln {u^n} = n\ln u\, \hfill \\
y = \frac{3}{2}\ln \left( {5{x^3} - 2x} \right) \hfill \\
Differentiate \hfill \\
{y^,} = \,\,{\left[ {\frac{3}{2}\ln \left( {5{x^3} - 2x} \right)} \right]^,} \hfill \\
Pull\,\,out\,\,the\,\,constant \hfill \\
{y^,} = \frac{3}{2}\,\,\left[ {\ln \left( {5{x^3} - 2x} \right)} \right] \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {\ln g\,\left( x \right)} \right] = \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\
Then \hfill \\
{y^,} = \frac{3}{2}\,\left( {\frac{{\,{{\left( {5{x^3} - 2x} \right)}^,}}}{{5{x^3} - 2x}}} \right) \hfill \\
{y^,} = \frac{3}{2}\,\left( {\frac{{15{x^2} - 2}}{{5{x^3} - 2x}}} \right) \hfill \\
\hfill \\
\end{gathered} \]
