Answer
\[{y^,} = 1.2{e^{ - 0.3x}}\]
Work Step by Step
\[\begin{gathered}
y = - 4{e^{ - 0.3x}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,\left( { - 4{e^{ - 0.3x}}} \right) \hfill \\
{y^,} = - 4\,\left( {{e^{ - 0.3x}}} \right) \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{y^,} = \, - 4\,\left( {{e^{ - 0.3x}}\,} \right)\,{\left( { - 0.3x} \right)^,} \hfill \\
{y^,} = - 4\,\left( {{e^{ - 0.3x}}\,} \right)\,\left( { - 0.3} \right) \hfill \\
Multiplying\, \hfill \\
{y^,} = 1.2{e^{ - 0.3x}} \hfill \\
\end{gathered} \]
