If \(f:\mathbb{R}-\{0\}\rightarrow\mathbb{R}\) is a differentiable function such that
\[
\frac{1}{3}f(x)+3f\!\left(\frac1x\right)
=
x-\frac{10}{3},
\]
then find
\[
f'(3)-f'\!\left(\frac13\right).
\]
Show Hint
For equations involving both \(f(x)\) and \(f(1/x)\), always replace \(x\) by \(1/x\) to obtain a second equation. Solving the resulting system usually leads directly to an explicit formula for \(f(x)\).