If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).
Show Hint
The derivative of \(\log(\frac{a+bx}{a-bx})\) is always \(\frac{2ab}{a^2 - b^2x^2}\). Memorizing this pattern helps in solving differentiation problems quickly without doing the full quotient rule!