<PRELOAD>
miniaufgabe.js
</PRELOAD>


==== 10. September 2018 bis 14. September 2018 ====
=== Montag 10. September 2018 ===
Berechnen Sie und kürzen Sie das Resultat vollständig.
<JS>miniAufgabe("#exobruchrechnen2","#solbruchrechnen2",
[["$$\\left(\\frac{5}{4}+\\frac{7}{5}\\right)\\cdot\\left(-\\frac{50}{53}\\right)$$", "$$\\left(\\frac{25}{20}+\\frac{28}{20}\\right)\\cdot-\\frac{50}{53}=\\frac{53}{20}\\cdot-\\frac{50}{53}=-\\frac{5}{2}$$"], ["$$\\frac{3}{2}:\\frac{9}{5}-\\frac{1}{3}$$", "$$\\frac{5}{6}-\\frac{1}{3}=\\frac{5}{6}-\\frac{2}{6}=\\frac{1}{2}$$"], ["$$-\\frac{7}{5}:\\left(-\\frac{84}{55}\\right)+\\frac{1}{3}$$", "$$\\frac{11}{12}+\\frac{1}{3}=\\frac{11}{12}+\\frac{4}{12}=\\frac{5}{4}$$"], ["$$\\frac{8}{5}\\cdot\\frac{25}{48}+\\frac{5}{3}$$", "$$\\frac{5}{6}+\\frac{5}{3}=\\frac{5}{6}+\\frac{10}{6}=\\frac{5}{2}$$"], ["$$-\\frac{3}{2}:\\left(-\\frac{45}{8}\\right)+\\frac{7}{5}$$", "$$\\frac{4}{15}+\\frac{7}{5}=\\frac{4}{15}+\\frac{21}{15}=\\frac{5}{3}$$"], ["$$\\left(\\frac{7}{4}+\\frac{8}{5}\\right):\\frac{67}{70}$$", "$$\\left(\\frac{35}{20}+\\frac{32}{20}\\right):\\frac{67}{70}=\\frac{67}{20}:\\frac{67}{70}=\\frac{7}{2}$$"], ["$$\\frac{3}{2}:\\left(-\\frac{9}{4}\\right)+\\frac{7}{6}$$", "$$-\\frac{2}{3}+\\frac{7}{6}=-\\frac{4}{6}+\\frac{7}{6}=\\frac{1}{2}$$"], ["$$\\frac{6}{5}:\\frac{12}{43}-\\frac{7}{2}$$", "$$\\frac{43}{10}-\\frac{7}{2}=\\frac{43}{10}-\\frac{35}{10}=\\frac{4}{5}$$"], ["$$\\left(\\frac{7}{6}+\\frac{7}{3}\\right)\\cdot\\left(-\\frac{1}{7}\\right)$$", "$$\\left(\\frac{7}{6}+\\frac{14}{6}\\right)\\cdot-\\frac{1}{7}=\\frac{7}{2}\\cdot-\\frac{1}{7}=-\\frac{1}{2}$$"], ["$$-\\frac{9}{5}\\cdot\\frac{5}{27}+\\frac{3}{2}$$", "$$-\\frac{1}{3}+\\frac{3}{2}=-\\frac{2}{6}+\\frac{9}{6}=\\frac{7}{6}$$"]],
" &nbsp; &nbsp; ");
</JS>
<HTML>
<div id="exobruchrechnen2"></div>

</HTML>
<hidden Lösungen>
<HTML>
<div id="solbruchrechnen2"></div>
</HTML>
</hidden>


=== Donnerstag 13. September 2018 ===

Berechnen Sie von Hand. Im Resultat sind alle Brüche gekürzt.
<JS>miniAufgabe("#exovectolength","#solvectolength",
[["$\\begin{pmatrix} \\frac{6}{5} \\\\ \\frac{2}{3} \\\\ -\\frac{5}{6}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{2}{5} \\\\ -\\frac{2}{3} \\\\ \\frac{4}{3}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{6}{5} \\\\ \\frac{2}{3} \\\\ -\\frac{5}{6}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{2}{5} \\\\ -\\frac{2}{3} \\\\ \\frac{4}{3}\\end{pmatrix}  = \\begin{pmatrix}\\frac{2}{3} \\cdot \\frac{4}{3} & - & \\left(-\\frac{5}{6}\\right) \\cdot \\left(-\\frac{2}{3}\\right) \\\\ -\\frac{5}{6} \\cdot \\left(-\\frac{2}{5}\\right) & - & \\frac{6}{5} \\cdot \\frac{4}{3} \\\\ \\frac{6}{5} \\cdot \\left(-\\frac{2}{3}\\right) & - & \\frac{2}{3} \\cdot \\left(-\\frac{2}{5}\\right)\\end{pmatrix} = \\begin{pmatrix}\\frac{8}{9} & - &  \\frac{5}{9} \\\\ \\frac{1}{3} & - &  \\frac{8}{5} \\\\ -\\frac{4}{5} & - &  \\left(-\\frac{4}{15}\\right)\\end{pmatrix} = \\begin{pmatrix} \\frac{1}{3} \\\\ -\\frac{19}{15} \\\\ -\\frac{8}{15}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{2}{5} \\\\ -\\frac{5}{3} \\\\ \\frac{5}{6}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{2}{5} \\\\ -\\frac{2}{3} \\\\ \\frac{2}{3}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{2}{5} \\\\ -\\frac{5}{3} \\\\ \\frac{5}{6}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{2}{5} \\\\ -\\frac{2}{3} \\\\ \\frac{2}{3}\\end{pmatrix}  = \\begin{pmatrix}-\\frac{5}{3} \\cdot \\frac{2}{3} & - & \\frac{5}{6} \\cdot \\left(-\\frac{2}{3}\\right) \\\\ \\frac{5}{6} \\cdot \\frac{2}{5} & - & \\frac{2}{5} \\cdot \\frac{2}{3} \\\\ \\frac{2}{5} \\cdot \\left(-\\frac{2}{3}\\right) & - & \\left(-\\frac{5}{3}\\right) \\cdot \\frac{2}{5}\\end{pmatrix} = \\begin{pmatrix}-\\frac{10}{9} & - &  \\left(-\\frac{5}{9}\\right) \\\\ \\frac{1}{3} & - &  \\frac{4}{15} \\\\ -\\frac{4}{15} & - &  \\left(-\\frac{2}{3}\\right)\\end{pmatrix} = \\begin{pmatrix} -\\frac{5}{9} \\\\ \\frac{1}{15} \\\\ \\frac{2}{5}\\end{pmatrix} $"], ["$\\begin{pmatrix} -\\frac{7}{9} \\\\ -\\frac{7}{3} \\\\ \\frac{5}{9}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{6}{5} \\\\ \\frac{3}{5} \\\\ \\frac{3}{4}\\end{pmatrix} $", "$\\begin{pmatrix} -\\frac{7}{9} \\\\ -\\frac{7}{3} \\\\ \\frac{5}{9}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{6}{5} \\\\ \\frac{3}{5} \\\\ \\frac{3}{4}\\end{pmatrix}  = \\begin{pmatrix}-\\frac{7}{3} \\cdot \\frac{3}{4} & - & \\frac{5}{9} \\cdot \\frac{3}{5} \\\\ \\frac{5}{9} \\cdot \\frac{6}{5} & - & \\left(-\\frac{7}{9}\\right) \\cdot \\frac{3}{4} \\\\ -\\frac{7}{9} \\cdot \\frac{3}{5} & - & \\left(-\\frac{7}{3}\\right) \\cdot \\frac{6}{5}\\end{pmatrix} = \\begin{pmatrix}-\\frac{7}{4} & - &  \\frac{1}{3} \\\\ \\frac{2}{3} & - &  \\left(-\\frac{7}{12}\\right) \\\\ -\\frac{7}{15} & - &  \\left(-\\frac{14}{5}\\right)\\end{pmatrix} = \\begin{pmatrix} -\\frac{25}{12} \\\\ \\frac{5}{4} \\\\ \\frac{7}{3}\\end{pmatrix} $"], ["$\\begin{pmatrix} -\\frac{2}{3} \\\\ -\\frac{2}{5} \\\\ \\frac{6}{5}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{2}{3} \\\\ -\\frac{3}{5} \\\\ \\frac{4}{5}\\end{pmatrix} $", "$\\begin{pmatrix} -\\frac{2}{3} \\\\ -\\frac{2}{5} \\\\ \\frac{6}{5}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{2}{3} \\\\ -\\frac{3}{5} \\\\ \\frac{4}{5}\\end{pmatrix}  = \\begin{pmatrix}-\\frac{2}{5} \\cdot \\frac{4}{5} & - & \\frac{6}{5} \\cdot \\left(-\\frac{3}{5}\\right) \\\\ \\frac{6}{5} \\cdot \\frac{2}{3} & - & \\left(-\\frac{2}{3}\\right) \\cdot \\frac{4}{5} \\\\ -\\frac{2}{3} \\cdot \\left(-\\frac{3}{5}\\right) & - & \\left(-\\frac{2}{5}\\right) \\cdot \\frac{2}{3}\\end{pmatrix} = \\begin{pmatrix}-\\frac{8}{25} & - &  \\left(-\\frac{18}{25}\\right) \\\\ \\frac{4}{5} & - &  \\left(-\\frac{8}{15}\\right) \\\\ \\frac{2}{5} & - &  \\left(-\\frac{4}{15}\\right)\\end{pmatrix} = \\begin{pmatrix} \\frac{2}{5} \\\\ \\frac{4}{3} \\\\ \\frac{2}{3}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{5}{3} \\\\ \\frac{2}{5} \\\\ -\\frac{7}{6}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{6} \\\\ -\\frac{4}{3} \\\\ \\frac{5}{6}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{5}{3} \\\\ \\frac{2}{5} \\\\ -\\frac{7}{6}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{6} \\\\ -\\frac{4}{3} \\\\ \\frac{5}{6}\\end{pmatrix}  = \\begin{pmatrix}\\frac{2}{5} \\cdot \\frac{5}{6} & - & \\left(-\\frac{7}{6}\\right) \\cdot \\left(-\\frac{4}{3}\\right) \\\\ -\\frac{7}{6} \\cdot \\left(-\\frac{5}{6}\\right) & - & \\frac{5}{3} \\cdot \\frac{5}{6} \\\\ \\frac{5}{3} \\cdot \\left(-\\frac{4}{3}\\right) & - & \\frac{2}{5} \\cdot \\left(-\\frac{5}{6}\\right)\\end{pmatrix} = \\begin{pmatrix}\\frac{1}{3} & - &  \\frac{14}{9} \\\\ \\frac{35}{36} & - &  \\frac{25}{18} \\\\ -\\frac{20}{9} & - &  \\left(-\\frac{1}{3}\\right)\\end{pmatrix} = \\begin{pmatrix} -\\frac{11}{9} \\\\ -\\frac{5}{12} \\\\ -\\frac{17}{9}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{3}{4} \\\\ -\\frac{3}{4} \\\\ \\frac{3}{10}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{3} \\\\ \\frac{5}{6} \\\\ \\frac{4}{9}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{3}{4} \\\\ -\\frac{3}{4} \\\\ \\frac{3}{10}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{3} \\\\ \\frac{5}{6} \\\\ \\frac{4}{9}\\end{pmatrix}  = \\begin{pmatrix}-\\frac{3}{4} \\cdot \\frac{4}{9} & - & \\frac{3}{10} \\cdot \\frac{5}{6} \\\\ \\frac{3}{10} \\cdot \\left(-\\frac{5}{3}\\right) & - & \\frac{3}{4} \\cdot \\frac{4}{9} \\\\ \\frac{3}{4} \\cdot \\frac{5}{6} & - & \\left(-\\frac{3}{4}\\right) \\cdot \\left(-\\frac{5}{3}\\right)\\end{pmatrix} = \\begin{pmatrix}-\\frac{1}{3} & - &  \\frac{1}{4} \\\\ -\\frac{1}{2} & - &  \\frac{1}{3} \\\\ \\frac{5}{8} & - &  \\frac{5}{4}\\end{pmatrix} = \\begin{pmatrix} -\\frac{7}{12} \\\\ -\\frac{5}{6} \\\\ -\\frac{5}{8}\\end{pmatrix} $"], ["$\\begin{pmatrix} -\\frac{7}{9} \\\\ \\frac{2}{3} \\\\ \\frac{5}{4}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{5}{9} \\\\ -\\frac{4}{3} \\\\ -\\frac{4}{7}\\end{pmatrix} $", "$\\begin{pmatrix} -\\frac{7}{9} \\\\ \\frac{2}{3} \\\\ \\frac{5}{4}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{5}{9} \\\\ -\\frac{4}{3} \\\\ -\\frac{4}{7}\\end{pmatrix}  = \\begin{pmatrix}\\frac{2}{3} \\cdot \\left(-\\frac{4}{7}\\right) & - & \\frac{5}{4} \\cdot \\left(-\\frac{4}{3}\\right) \\\\ \\frac{5}{4} \\cdot \\frac{5}{9} & - & \\left(-\\frac{7}{9}\\right) \\cdot \\left(-\\frac{4}{7}\\right) \\\\ -\\frac{7}{9} \\cdot \\left(-\\frac{4}{3}\\right) & - & \\frac{2}{3} \\cdot \\frac{5}{9}\\end{pmatrix} = \\begin{pmatrix}-\\frac{8}{21} & - &  \\left(-\\frac{5}{3}\\right) \\\\ \\frac{25}{36} & - &  \\frac{4}{9} \\\\ \\frac{28}{27} & - &  \\frac{10}{27}\\end{pmatrix} = \\begin{pmatrix} \\frac{9}{7} \\\\ \\frac{1}{4} \\\\ \\frac{2}{3}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{3}{4} \\\\ -\\frac{3}{4} \\\\ \\frac{5}{8}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{6}{5} \\\\ -\\frac{2}{5} \\\\ -\\frac{5}{9}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{3}{4} \\\\ -\\frac{3}{4} \\\\ \\frac{5}{8}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{6}{5} \\\\ -\\frac{2}{5} \\\\ -\\frac{5}{9}\\end{pmatrix}  = \\begin{pmatrix}-\\frac{3}{4} \\cdot \\left(-\\frac{5}{9}\\right) & - & \\frac{5}{8} \\cdot \\left(-\\frac{2}{5}\\right) \\\\ \\frac{5}{8} \\cdot \\frac{6}{5} & - & \\frac{3}{4} \\cdot \\left(-\\frac{5}{9}\\right) \\\\ \\frac{3}{4} \\cdot \\left(-\\frac{2}{5}\\right) & - & \\left(-\\frac{3}{4}\\right) \\cdot \\frac{6}{5}\\end{pmatrix} = \\begin{pmatrix}\\frac{5}{12} & - &  \\left(-\\frac{1}{4}\\right) \\\\ \\frac{3}{4} & - &  \\left(-\\frac{5}{12}\\right) \\\\ -\\frac{3}{10} & - &  \\left(-\\frac{9}{10}\\right)\\end{pmatrix} = \\begin{pmatrix} \\frac{2}{3} \\\\ \\frac{7}{6} \\\\ \\frac{3}{5}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{2}{3} \\\\ \\frac{7}{5} \\\\ -\\frac{7}{3}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{7} \\\\ -\\frac{2}{3} \\\\ \\frac{5}{3}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{2}{3} \\\\ \\frac{7}{5} \\\\ -\\frac{7}{3}\\end{pmatrix}  \\times \\begin{pmatrix} -\\frac{5}{7} \\\\ -\\frac{2}{3} \\\\ \\frac{5}{3}\\end{pmatrix}  = \\begin{pmatrix}\\frac{7}{5} \\cdot \\frac{5}{3} & - & \\left(-\\frac{7}{3}\\right) \\cdot \\left(-\\frac{2}{3}\\right) \\\\ -\\frac{7}{3} \\cdot \\left(-\\frac{5}{7}\\right) & - & \\frac{2}{3} \\cdot \\frac{5}{3} \\\\ \\frac{2}{3} \\cdot \\left(-\\frac{2}{3}\\right) & - & \\frac{7}{5} \\cdot \\left(-\\frac{5}{7}\\right)\\end{pmatrix} = \\begin{pmatrix}\\frac{7}{3} & - &  \\frac{14}{9} \\\\ \\frac{5}{3} & - &  \\frac{10}{9} \\\\ -\\frac{4}{9} & - &  \\left(-1\\right)\\end{pmatrix} = \\begin{pmatrix} \\frac{7}{9} \\\\ \\frac{5}{9} \\\\ \\frac{5}{9}\\end{pmatrix} $"], ["$\\begin{pmatrix} \\frac{3}{4} \\\\ \\frac{3}{5} \\\\ -\\frac{7}{5}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{5}{4} \\\\ \\frac{7}{6} \\\\ -\\frac{7}{6}\\end{pmatrix} $", "$\\begin{pmatrix} \\frac{3}{4} \\\\ \\frac{3}{5} \\\\ -\\frac{7}{5}\\end{pmatrix}  \\times \\begin{pmatrix} \\frac{5}{4} \\\\ \\frac{7}{6} \\\\ -\\frac{7}{6}\\end{pmatrix}  = \\begin{pmatrix}\\frac{3}{5} \\cdot \\left(-\\frac{7}{6}\\right) & - & \\left(-\\frac{7}{5}\\right) \\cdot \\frac{7}{6} \\\\ -\\frac{7}{5} \\cdot \\frac{5}{4} & - & \\frac{3}{4} \\cdot \\left(-\\frac{7}{6}\\right) \\\\ \\frac{3}{4} \\cdot \\frac{7}{6} & - & \\frac{3}{5} \\cdot \\frac{5}{4}\\end{pmatrix} = \\begin{pmatrix}-\\frac{7}{10} & - &  \\left(-\\frac{49}{30}\\right) \\\\ -\\frac{7}{4} & - &  \\left(-\\frac{7}{8}\\right) \\\\ \\frac{7}{8} & - &  \\frac{3}{4}\\end{pmatrix} = \\begin{pmatrix} \\frac{14}{15} \\\\ -\\frac{7}{8} \\\\ \\frac{1}{8}\\end{pmatrix} $"]],
" <br><hr> ", "<br><hr>");
</JS>
<HTML>
<div id="exovectolength"></div>

</HTML>
<hidden Lösungen>
<HTML>
<div id="solvectolength"></div>
</HTML>
</hidden>


=== Freitag 14. September 2018 ===

Leiten Sie von Hand und ohne Unterlagen ab:
<JS>miniAufgabe("#exotrigpoly","#soltrigpoly",
[["a) $f(x)=\\frac{1}{5}\\cos\\left(-\\frac{1}{2}x^{4}-\\frac{1}{9}\\right)\\quad$ b) $f(x)=-\\frac{2}{3}\\sin\\left(\\frac{3}{2}x^{2}-\\frac{3}{5}x\\right)\\quad$ ", "a) $f'(x)=\\frac{1}{5} \\cdot \\left(-2x^{3}\\right) \\cdot -\\sin\\left(-\\frac{1}{2}x^{4}-\\frac{1}{9}\\right) = \\frac{2}{5}x^{3}\\cdot \\sin\\left(-\\frac{1}{2}x^{4}-\\frac{1}{9}\\right)$ <br> b) $f'(x)=-\\frac{2}{3} \\cdot \\left(3x-\\frac{3}{5}\\right) \\cdot \\cos\\left(\\frac{3}{2}x^{2}-\\frac{3}{5}x\\right) = \\left(-2x+\\frac{2}{5}\\right)\\cdot \\cos\\left(\\frac{3}{2}x^{2}-\\frac{3}{5}x\\right)$ <br> "], ["a) $f(x)=\\frac{1}{3}\\cos\\left(-\\frac{2}{3}x^{4}-\\frac{4}{5}x\\right)\\quad$ b) $f(x)=\\frac{3}{8}\\sin\\left(-\\frac{1}{3}x^{4}-\\frac{1}{2}x\\right)\\quad$ ", "a) $f'(x)=\\frac{1}{3} \\cdot \\left(-\\frac{8}{3}x^{3}-\\frac{4}{5}\\right) \\cdot -\\sin\\left(-\\frac{2}{3}x^{4}-\\frac{4}{5}x\\right) = \\left(\\frac{8}{9}x^{3}+\\frac{4}{15}\\right)\\cdot \\sin\\left(-\\frac{2}{3}x^{4}-\\frac{4}{5}x\\right)$ <br> b) $f'(x)=\\frac{3}{8} \\cdot \\left(-\\frac{4}{3}x^{3}-\\frac{1}{2}\\right) \\cdot \\cos\\left(-\\frac{1}{3}x^{4}-\\frac{1}{2}x\\right) = \\left(-\\frac{1}{2}x^{3}-\\frac{3}{16}\\right)\\cdot \\cos\\left(-\\frac{1}{3}x^{4}-\\frac{1}{2}x\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{3}\\cos\\left(\\frac{4}{5}x^{4}+\\frac{3}{5}x^{2}\\right)\\quad$ b) $f(x)=-\\frac{2}{7}\\sin\\left(\\frac{4}{3}x^{3}-\\frac{1}{8}x\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{3} \\cdot \\left(\\frac{16}{5}x^{3}+\\frac{6}{5}x\\right) \\cdot -\\sin\\left(\\frac{4}{5}x^{4}+\\frac{3}{5}x^{2}\\right) = \\left(\\frac{16}{15}x^{3}+\\frac{2}{5}x\\right)\\cdot \\sin\\left(\\frac{4}{5}x^{4}+\\frac{3}{5}x^{2}\\right)$ <br> b) $f'(x)=-\\frac{2}{7} \\cdot \\left(4x^{2}-\\frac{1}{8}\\right) \\cdot \\cos\\left(\\frac{4}{3}x^{3}-\\frac{1}{8}x\\right) = \\left(-\\frac{8}{7}x^{2}+\\frac{1}{28}\\right)\\cdot \\cos\\left(\\frac{4}{3}x^{3}-\\frac{1}{8}x\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{9}\\cos\\left(-\\frac{1}{3}x^{4}+\\frac{2}{5}x^{2}\\right)\\quad$ b) $f(x)=-\\frac{1}{4}\\sin\\left(-\\frac{1}{3}x^{2}-\\frac{1}{3}\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{9} \\cdot \\left(-\\frac{4}{3}x^{3}+\\frac{4}{5}x\\right) \\cdot -\\sin\\left(-\\frac{1}{3}x^{4}+\\frac{2}{5}x^{2}\\right) = \\left(-\\frac{4}{27}x^{3}+\\frac{4}{45}x\\right)\\cdot \\sin\\left(-\\frac{1}{3}x^{4}+\\frac{2}{5}x^{2}\\right)$ <br> b) $f'(x)=-\\frac{1}{4} \\cdot \\left(-\\frac{2}{3}x\\right) \\cdot \\cos\\left(-\\frac{1}{3}x^{2}-\\frac{1}{3}\\right) = \\frac{1}{6}x\\cdot \\cos\\left(-\\frac{1}{3}x^{2}-\\frac{1}{3}\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{4}\\cos\\left(\\frac{2}{5}x+\\frac{1}{7}\\right)\\quad$ b) $f(x)=\\frac{1}{4}\\sin\\left(-\\frac{1}{7}x^{4}-\\frac{2}{3}\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{4} \\cdot \\left(\\frac{2}{5}\\right) \\cdot -\\sin\\left(\\frac{2}{5}x+\\frac{1}{7}\\right) = \\frac{1}{10}\\cdot \\sin\\left(\\frac{2}{5}x+\\frac{1}{7}\\right)$ <br> b) $f'(x)=\\frac{1}{4} \\cdot \\left(-\\frac{4}{7}x^{3}\\right) \\cdot \\cos\\left(-\\frac{1}{7}x^{4}-\\frac{2}{3}\\right) = -\\frac{1}{7}x^{3}\\cdot \\cos\\left(-\\frac{1}{7}x^{4}-\\frac{2}{3}\\right)$ <br> "], ["a) $f(x)=\\frac{2}{3}\\cos\\left(-\\frac{1}{2}x^{2}+\\frac{2}{9}x\\right)\\quad$ b) $f(x)=-\\frac{4}{3}\\sin\\left(-\\frac{1}{2}x^{4}+\\frac{1}{2}x\\right)\\quad$ ", "a) $f'(x)=\\frac{2}{3} \\cdot \\left(-x+\\frac{2}{9}\\right) \\cdot -\\sin\\left(-\\frac{1}{2}x^{2}+\\frac{2}{9}x\\right) = \\left(\\frac{2}{3}x-\\frac{4}{27}\\right)\\cdot \\sin\\left(-\\frac{1}{2}x^{2}+\\frac{2}{9}x\\right)$ <br> b) $f'(x)=-\\frac{4}{3} \\cdot \\left(-2x^{3}+\\frac{1}{2}\\right) \\cdot \\cos\\left(-\\frac{1}{2}x^{4}+\\frac{1}{2}x\\right) = \\left(\\frac{8}{3}x^{3}-\\frac{2}{3}\\right)\\cdot \\cos\\left(-\\frac{1}{2}x^{4}+\\frac{1}{2}x\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{6}\\cos\\left(-\\frac{1}{3}x^{2}-\\frac{2}{9}\\right)\\quad$ b) $f(x)=\\frac{1}{4}\\sin\\left(-\\frac{3}{4}x^{2}-\\frac{1}{3}\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{6} \\cdot \\left(-\\frac{2}{3}x\\right) \\cdot -\\sin\\left(-\\frac{1}{3}x^{2}-\\frac{2}{9}\\right) = -\\frac{1}{9}x\\cdot \\sin\\left(-\\frac{1}{3}x^{2}-\\frac{2}{9}\\right)$ <br> b) $f'(x)=\\frac{1}{4} \\cdot \\left(-\\frac{3}{2}x\\right) \\cdot \\cos\\left(-\\frac{3}{4}x^{2}-\\frac{1}{3}\\right) = -\\frac{3}{8}x\\cdot \\cos\\left(-\\frac{3}{4}x^{2}-\\frac{1}{3}\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{3}\\cos\\left(\\frac{2}{5}x^{4}-\\frac{1}{4}x\\right)\\quad$ b) $f(x)=-\\frac{4}{5}\\sin\\left(\\frac{2}{3}x^{4}+\\frac{1}{3}x^{2}\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{3} \\cdot \\left(\\frac{8}{5}x^{3}-\\frac{1}{4}\\right) \\cdot -\\sin\\left(\\frac{2}{5}x^{4}-\\frac{1}{4}x\\right) = \\left(\\frac{8}{15}x^{3}-\\frac{1}{12}\\right)\\cdot \\sin\\left(\\frac{2}{5}x^{4}-\\frac{1}{4}x\\right)$ <br> b) $f'(x)=-\\frac{4}{5} \\cdot \\left(\\frac{8}{3}x^{3}+\\frac{2}{3}x\\right) \\cdot \\cos\\left(\\frac{2}{3}x^{4}+\\frac{1}{3}x^{2}\\right) = \\left(-\\frac{32}{15}x^{3}-\\frac{8}{15}x\\right)\\cdot \\cos\\left(\\frac{2}{3}x^{4}+\\frac{1}{3}x^{2}\\right)$ <br> "], ["a) $f(x)=\\frac{2}{5}\\cos\\left(-\\frac{2}{3}x^{2}+\\frac{2}{9}x\\right)\\quad$ b) $f(x)=-\\frac{1}{4}\\sin\\left(-\\frac{2}{7}x^{4}+\\frac{2}{7}\\right)\\quad$ ", "a) $f'(x)=\\frac{2}{5} \\cdot \\left(-\\frac{4}{3}x+\\frac{2}{9}\\right) \\cdot -\\sin\\left(-\\frac{2}{3}x^{2}+\\frac{2}{9}x\\right) = \\left(\\frac{8}{15}x-\\frac{4}{45}\\right)\\cdot \\sin\\left(-\\frac{2}{3}x^{2}+\\frac{2}{9}x\\right)$ <br> b) $f'(x)=-\\frac{1}{4} \\cdot \\left(-\\frac{8}{7}x^{3}\\right) \\cdot \\cos\\left(-\\frac{2}{7}x^{4}+\\frac{2}{7}\\right) = \\frac{2}{7}x^{3}\\cdot \\cos\\left(-\\frac{2}{7}x^{4}+\\frac{2}{7}\\right)$ <br> "], ["a) $f(x)=-\\frac{1}{9}\\cos\\left(-\\frac{1}{5}x^{2}-\\frac{3}{2}x\\right)\\quad$ b) $f(x)=-\\frac{2}{9}\\sin\\left(\\frac{1}{4}x^{4}+\\frac{1}{2}x^{3}\\right)\\quad$ ", "a) $f'(x)=-\\frac{1}{9} \\cdot \\left(-\\frac{2}{5}x-\\frac{3}{2}\\right) \\cdot -\\sin\\left(-\\frac{1}{5}x^{2}-\\frac{3}{2}x\\right) = \\left(-\\frac{2}{45}x-\\frac{1}{6}\\right)\\cdot \\sin\\left(-\\frac{1}{5}x^{2}-\\frac{3}{2}x\\right)$ <br> b) $f'(x)=-\\frac{2}{9} \\cdot \\left(x^{3}+\\frac{3}{2}x^{2}\\right) \\cdot \\cos\\left(\\frac{1}{4}x^{4}+\\frac{1}{2}x^{3}\\right) = \\left(-\\frac{2}{9}x^{3}-\\frac{1}{3}x^{2}\\right)\\cdot \\cos\\left(\\frac{1}{4}x^{4}+\\frac{1}{2}x^{3}\\right)$ <br> "]],
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