Instrucciones: Responde las siguientes preguntas.

• Deriva la función \(y = \frac{5x+4}{3x^{2}+5x+1}\) con respecto a \(x\).
  • $$y^{\prime} = -\frac{11x^{2}+25x+11}{\left ( 3x^{2}+5x+1 \right )^{2}}$$
  • $$y^{\prime} = -\frac{15x^{2}+24x+15}{\left ( 3x^{2}+5x+1 \right )^{2}}$$
  • $$y^{\prime} = \frac{17x^{2}+22x+17}{\left ( 3x^{2}+5x+1 \right )^{2}}$$
  • $$y^{\prime} = \frac{22x^{2}+31x+22}{\left ( 3x^{2}+5x+1 \right )^{2}}$$

• Deriva la función \(y = \frac{5x^{2}+6x-7}{-6x^{3}-6x^{2}+8x}\) con respecto a \(x\).
  • $$y^{\prime} = -\frac{16x^{4}+42x^{3}-12x^{2}-41x+15}{\left ( 3x^{2}+3x-4 \right )^{2}}$$
  • $$y^{\prime} = -\frac{19x^{4}+30x^{3}-21x^{2}-34x+13}{\left ( 3x^{2}+3x-4 \right )^{2}}$$
  • $$y^{\prime} = \frac{15x^{4}+36x^{3}-25x^{2}-42x+28}{2x^{2}\left ( 3x^{2}+3x-4 \right )^{2}}$$
  • $$y^{\prime} = \frac{21x^{4}+40x^{3}-37x^{2}-52x+37}{2x^{2}\left ( 3x^{2}+3x-4 \right )^{2}}$$

• Deriva la función \(y = \frac{-2x^{2}-3x+7}{x+9}\) con respecto a \(x\).
  • $$y^{\prime} = \frac{4x^{2}+34x+36}{\left ( x+9 \right )^{2}}$$
  • $$y^{\prime} = -\frac{9x^{2}+41x+26}{\left ( x+9 \right )^{2}}$$
  • $$y^{\prime} = \frac{3x^{2}+45x+48}{\left ( x+9 \right )^{2}}$$
  • $$y^{\prime} = -\frac{2x^{2}+36x+34}{\left ( x+9 \right )^{2}}$$

• Deriva la función \(y = \frac{6x^{2}+10x+1}{8x-9}\) con respecto a \(x\).
  • $$y^{\prime} = -\frac{62x^{2}-57x-73}{\left ( 8x-9 \right )^{2}}$$
  • $$y^{\prime} = \frac{48x^{2}-108x-98}{\left ( 8x-9 \right )^{2}}$$
  • $$y^{\prime} = -\frac{58x^{2}-90x-111}{\left ( 8x-9 \right )^{2}}$$
  • $$y^{\prime} = \frac{68x^{2}-136x-100}{\left ( 8x-9 \right )^{2}}$$

• Deriva la función \(y = \frac{6x}{7x^{2}-x-7}\) con respecto a \(x\).
  • $$y^{\prime} = \frac{40x^{2}+40}{\left ( 7x^{2}-x-7 \right )^{2}}$$
  • $$y^{\prime} = -\frac{60x^{2}+60}{\left ( 7x^{2}-x-7 \right )^{2}}$$
  • $$y^{\prime} = -\frac{42x^{2}+42}{\left ( 7x^{2}-x-7 \right )^{2}}$$
  • $$y^{\prime} = \frac{38x^{2}+38}{\left ( 7x^{2}-x-7 \right )^{2}}$$