Lời giải

• \(g(x) = f\left(\frac{5x}{x^2 + 4}\right) \)
• \( \left(\frac{5x}{x^2 + 4}\right)' = \frac{5(4-x^2 )}{(x^2 + 4)^2}\)
• \(g'(x) = \frac{5(4-x^2)}{(x^2 + 4)^2} \cdot f'\left(\frac{5x}{x^2 + 4}\right) \)

\( =  \frac{5(4 - x^2)}{(x^2 + 4)^2} \cdot \left( \frac{5x}{x^2 + 4} \right)^2  \)

\(\quad \cdot \left( \frac{5x}{x^2 + 4} -1 \right) \cdot  \left( \frac{65x}{x^2 + 4} - 15 \right)^3 \)

\(= \frac{5(4 - x^2)}{(x^2 + 4)^2} \left( \frac{5x}{x^2 + 4} \right)^2 \)

\( \quad \left(  \frac{-x^2+ 5x - 4}{(x^2 + 4)} \right) \left( \frac{15(-x^2 + 13x - 4)}{x^2 + 4} \right)^3 \)

\( = \frac{5 (2-x)(2+x)}{(x + 4)^2} \left( \frac{5x}{x^2 + 4} \right)^2 \)

\( \quad \left( \frac{-(x - 1)(x - 4)}{x^2 + 4} \right) - \left[ \frac{15 \left( x - \frac{13 - 3 \sqrt{17}}{2} \right) \left( x - \frac{13 +3 \sqrt{17}}{2} \right) }{x^2 + 4} \right] ^3\)

\(g'(x) \) đổi dấu 6 lần. Chọn \(\boxed{D}\).