#### Answer

\[{y^,} = - 6x\ln 10\,\left( {{{10}^{3{x^2} - 4}}} \right)\]

#### Work Step by Step

\[\begin{gathered}
y = - {10^{3{x^2} - 4}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,{\left( { - {{10}^{3{x^2} - 4}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Set\,\,a = 10\,,\,g\,\left( x \right) = 3{x^2} - 4 \hfill \\
Then \hfill \\
{y^,} = \, - \,\left( {\ln 10} \right)\,\left( {{{10}^{3{x^2} - 4}}} \right)\,{\left( {3{x^2} - 4} \right)^,} \hfill \\
{y^,} = - \,\left( {\ln 10} \right)\,\left( {{{10}^{3{x^2} - 4}}} \right)\,\left( {6x} \right) \hfill \\
Multiplying \hfill \\
{y^,} = - 6x\ln 10\,\left( {{{10}^{3{x^2} - 4}}} \right) \hfill \\
\end{gathered} \]