#### Answer

\[{y^,} = 15{x^2} - 14x - 9\]

#### Work Step by Step

\[\begin{gathered}
y = 5{x^3} - 7{x^2} - 9x + \sqrt 5 \hfill \\
Find\,\,the\,\,derivative\,\,of\,\,the\,\,function \hfill \\
{y^,} = \frac{d}{{dx}}\,\,\left[ {5{x^3} - 7{x^2} - 9x + \sqrt 5 } \right] \hfill \\
Use\,\,the\,\,formula\,\,\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\
Then \hfill \\
{y^,} = 5\,\left( 3 \right){x^{3 - 1}} - 7\,\left( 2 \right){x^{2 - 1}} - 9\,\left( 1 \right) + 0 \hfill \\
Simplifying \hfill \\
{y^,} = 15{x^2} - 14x - 9 \hfill \\
\end{gathered} \]