#### Answer

\[{y^,} = - 5\ln 4\,\left( {{4^{ - 5x + 2}}} \right)\]

#### Work Step by Step

\[\begin{gathered}
y = {4^{ - 5x + 2}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,{\left( {{4^{ - 5x + 2}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
Let\,\,a = 4\,,\,g\,\left( x \right) = - 5x + 2 \hfill \\
{y^,} = \,\left( {\ln 4} \right){4^{ - 5x + 2}}\,{\left( {5x + 2} \right)^,} \hfill \\
{y^,} = \,\left( {\ln 4} \right)\,\left( {{4^{ - 5x + 2}}} \right)\,\left( { - 5} \right) \hfill \\
Multiplying \hfill \\
{y^,} = - 5\ln 4\,\left( {{4^{ - 5x + 2}}} \right) \hfill \\
\end{gathered} \]