#### Answer

\[{y^,} = 2x{e^{{x^2}}}\]

#### Work Step by Step

\[\begin{gathered}
y = {e^{{x^2}}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,{\left( {{e^{{x^2}}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{y^,} = \left( {{e^{{x^2}}}} \right)\,{\left( {{x^2}} \right)^,} \hfill \\
{y^,} = \,\left( {{e^{{x^2}}}} \right)\,\left( {2x} \right) \hfill \\
Multiplying\, \hfill \\
{y^,} = 2x{e^{{x^2}}} \hfill \\
\end{gathered} \]