\(\begin{array}{l}
1)\quad y = \dfrac{2x+3}{4x}\\
\to y' = \dfrac{(2x+3)'.4x - (2x+3).(4x)'}{16x^2}\\
\to y' = \dfrac{2.4x - (2x+3).4}{16x^2}\\
\to y' = \dfrac{8x - (8x + 12)}{16x^2}\\
\to y' = \dfrac{-12}{16x^2}\\
\to y' = - \dfrac{3}{4x^2}\\
2)\quad y = \dfrac{2x+3x^2 - 2}{4x+5}\\
\to y' = \dfrac{(2x + 3x^2 - 2)'(4x + 5) - (2x + 3x^2 - 2)(4x+5)'}{(4x+5)^2}\\
\to y' = \dfrac{(6x + 2)(4x+5) - (2x + 3x^2 - 2).4}{(4x+5)^2}\\
\to y' = \dfrac{24x^2 + 38x + 10 - (12x^2 + 8x - 8)}{(4x+5)^2}\\
\to y' = \dfrac{12x^2 + 30x + 18}{(4x+5)^2}
\end{array}\)
