Take the derivative of the equation to find the rate of change of the equation:

\(\displaystyle{C}'{\left({x}\right)}={\left(\frac{{1}}{{2}}\right)}\times{18}{x}^{{\frac{{1}}{{2}}-{1}}}\)

Simplify:

\(\displaystyle{C}'{\left({x}\right)}={9}{x}^{{-\frac{{1}}{{2}}}}\)

Substitute x=500:

\(\displaystyle{C}'{\left({500}\right)}={9}{\left[{500}\right)}^{{-\frac{{1}}{{2}}}}{]}\)

simplify:

\(\displaystyle{C}'{\left({500}\right)}\approx{0.4025}\)

=40.25%

\(\displaystyle{C}'{\left({x}\right)}={\left(\frac{{1}}{{2}}\right)}\times{18}{x}^{{\frac{{1}}{{2}}-{1}}}\)

Simplify:

\(\displaystyle{C}'{\left({x}\right)}={9}{x}^{{-\frac{{1}}{{2}}}}\)

Substitute x=500:

\(\displaystyle{C}'{\left({500}\right)}={9}{\left[{500}\right)}^{{-\frac{{1}}{{2}}}}{]}\)

simplify:

\(\displaystyle{C}'{\left({500}\right)}\approx{0.4025}\)

=40.25%