#### Answer

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

#### Work Step by Step

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