If
\[
y=\tan^{-1}\!\left(\frac{\sqrt{1+9x^{2}}-1}{3x}\right),
\]
then
\[
\left(\frac{dy}{dx}\right)_{x=\frac1{\sqrt3}}
=
\]
Show Hint
Whenever an inverse trigonometric function contains an expression of the form
\[
\frac{\sqrt{1+a^{2}x^{2}}-1}{ax},
\]
first rationalize the numerator. The resulting expression becomes much easier to differentiate using the chain rule.