Homework$-8$: Problem $1$

$(6$ points$)$

Find the derivative of $f(x)=-\frac{\sqrt[\phantom{2}]{x^2+9}}{9x}+C$ to complete the following integration formula:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x^2\sqrt[\phantom{2}]{x^2+9}}dx=-\frac{\sqrt[\phantom{2}]{x^2+9}}{9x}+C$