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miniaufgabe.js
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==== 2. September 2019 bis 6. September 2019 ====
=== Dienstag 3. September 2019 ===
Ausfall, English-Exam
=== Donnerstag 5. September 2019 ===
Leiten Sie von Hand und ohne Unterlagen ab:
<JS>miniAufgabe("#exolincomb_exp_log_power","#sollincomb_exp_log_power",
[["$f(x)=\\frac{3}{7}\\cdot\\left(x^{-\\frac{7}{6}} +\\frac{28}{15}\\cdot \\left(\\mathrm{e}^x +\\frac{5}{24}\\cdot \\ln(x)\\right) -\\frac{28}{27}\\right)$", "$f'(x) = \\left(\\frac{3}{7}\\cdot x^{-\\frac{7}{6}} + \\frac{4}{5}\\mathrm{e}^x +\\frac{1}{6}\\ln(x) + -\\frac{4}{9}\\right)' = \\frac{3}{7} \\cdot \\left(-\\frac{7}{6}\\right) \\cdot x^{-\\frac{13}{6}} +\\frac{4}{5} \\cdot \\mathrm{e}^x +\\frac{1}{6}\\cdot \\frac{1}{x} + 0 = -\\frac{1}{2} \\cdot x^{-\\frac{13}{6}} +\\frac{4}{5} \\cdot \\mathrm{e}^x +\\frac{1}{6}\\cdot \\frac{1}{x}$"], ["$f(x)=-\\frac{4}{7}\\cdot\\left(x^{-\\frac{7}{12}} -\\frac{21}{16}\\cdot \\left(\\mathrm{e}^x -\\frac{4}{9}\\cdot \\ln(x)\\right) +\\frac{7}{6}\\right)$", "$f'(x) = \\left(-\\frac{4}{7}\\cdot x^{-\\frac{7}{12}} + \\frac{3}{4}\\mathrm{e}^x +-\\frac{1}{3}\\ln(x) + -\\frac{2}{3}\\right)' = -\\frac{4}{7} \\cdot \\left(-\\frac{7}{12}\\right) \\cdot x^{-\\frac{19}{12}} +\\frac{3}{4} \\cdot \\mathrm{e}^x -\\frac{1}{3}\\cdot \\frac{1}{x} + 0 = \\frac{1}{3} \\cdot x^{-\\frac{19}{12}} +\\frac{3}{4} \\cdot \\mathrm{e}^x -\\frac{1}{3}\\cdot \\frac{1}{x}$"], ["$f(x)=-\\frac{4}{7}\\cdot\\left(x^{\\frac{7}{8}} +\\frac{7}{9}\\cdot \\left(\\mathrm{e}^x +\\frac{3}{4}\\cdot \\ln(x)\\right) +\\frac{7}{18}\\right)$", "$f'(x) = \\left(-\\frac{4}{7}\\cdot x^{\\frac{7}{8}} + -\\frac{4}{9}\\mathrm{e}^x +-\\frac{1}{3}\\ln(x) + -\\frac{2}{9}\\right)' = -\\frac{4}{7} \\cdot \\frac{7}{8} \\cdot x^{-\\frac{1}{8}} -\\frac{4}{9} \\cdot \\mathrm{e}^x -\\frac{1}{3}\\cdot \\frac{1}{x} + 0 = -\\frac{1}{2} \\cdot x^{-\\frac{1}{8}} -\\frac{4}{9} \\cdot \\mathrm{e}^x -\\frac{1}{3}\\cdot \\frac{1}{x}$"], ["$f(x)=-\\frac{1}{2}\\cdot\\left(x^{\\frac{6}{7}} +\\frac{2}{3}\\cdot \\left(\\mathrm{e}^x -\\frac{1}{3}\\cdot \\ln(x)\\right) +\\frac{4}{7}\\right)$", "$f'(x) = \\left(-\\frac{1}{2}\\cdot x^{\\frac{6}{7}} + -\\frac{1}{3}\\mathrm{e}^x +\\frac{1}{9}\\ln(x) + -\\frac{2}{7}\\right)' = -\\frac{1}{2} \\cdot \\frac{6}{7} \\cdot x^{-\\frac{1}{7}} -\\frac{1}{3} \\cdot \\mathrm{e}^x +\\frac{1}{9}\\cdot \\frac{1}{x} + 0 = -\\frac{3}{7} \\cdot x^{-\\frac{1}{7}} -\\frac{1}{3} \\cdot \\mathrm{e}^x +\\frac{1}{9}\\cdot \\frac{1}{x}$"], ["$f(x)=\\frac{1}{6}\\cdot\\left(x^{\\frac{6}{5}} -\\frac{3}{4}\\cdot \\left(\\mathrm{e}^x +\\frac{24}{5}\\cdot \\ln(x)\\right) +\\frac{3}{2}\\right)$", "$f'(x) = \\left(\\frac{1}{6}\\cdot x^{\\frac{6}{5}} + -\\frac{1}{8}\\mathrm{e}^x +-\\frac{3}{5}\\ln(x) + \\frac{1}{4}\\right)' = \\frac{1}{6} \\cdot \\frac{6}{5} \\cdot x^{\\frac{1}{5}} -\\frac{1}{8} \\cdot \\mathrm{e}^x -\\frac{3}{5}\\cdot \\frac{1}{x} + 0 = \\frac{1}{5} \\cdot x^{\\frac{1}{5}} -\\frac{1}{8} \\cdot \\mathrm{e}^x -\\frac{3}{5}\\cdot \\frac{1}{x}$"], ["$f(x)=\\frac{1}{3}\\cdot\\left(x^{\\frac{3}{2}} -\\frac{1}{3}\\cdot \\left(\\mathrm{e}^x -\\frac{27}{7}\\cdot \\ln(x)\\right) -\\frac{9}{8}\\right)$", "$f'(x) = \\left(\\frac{1}{3}\\cdot x^{\\frac{3}{2}} + -\\frac{1}{9}\\mathrm{e}^x +\\frac{3}{7}\\ln(x) + -\\frac{3}{8}\\right)' = \\frac{1}{3} \\cdot \\frac{3}{2} \\cdot x^{\\frac{1}{2}} -\\frac{1}{9} \\cdot \\mathrm{e}^x +\\frac{3}{7}\\cdot \\frac{1}{x} + 0 = \\frac{1}{2} \\cdot x^{\\frac{1}{2}} -\\frac{1}{9} \\cdot \\mathrm{e}^x +\\frac{3}{7}\\cdot \\frac{1}{x}$"], ["$f(x)=\\frac{1}{2}\\cdot\\left(x^{-\\frac{1}{2}} -\\frac{6}{5}\\cdot \\left(\\mathrm{e}^x -\\frac{10}{9}\\cdot \\ln(x)\\right) -\\frac{8}{3}\\right)$", "$f'(x) = \\left(\\frac{1}{2}\\cdot x^{-\\frac{1}{2}} + -\\frac{3}{5}\\mathrm{e}^x +\\frac{2}{3}\\ln(x) + -\\frac{4}{3}\\right)' = \\frac{1}{2} \\cdot \\left(-\\frac{1}{2}\\right) \\cdot x^{-\\frac{3}{2}} -\\frac{3}{5} \\cdot \\mathrm{e}^x +\\frac{2}{3}\\cdot \\frac{1}{x} + 0 = -\\frac{1}{4} \\cdot x^{-\\frac{3}{2}} -\\frac{3}{5} \\cdot \\mathrm{e}^x +\\frac{2}{3}\\cdot \\frac{1}{x}$"], ["$f(x)=\\frac{2}{7}\\cdot\\left(x^{-\\frac{14}{3}} -\\frac{3}{2}\\cdot \\left(\\mathrm{e}^x -\\frac{7}{6}\\cdot \\ln(x)\\right) +\\frac{1}{2}\\right)$", "$f'(x) = \\left(\\frac{2}{7}\\cdot x^{-\\frac{14}{3}} + -\\frac{3}{7}\\mathrm{e}^x +\\frac{1}{2}\\ln(x) + \\frac{1}{7}\\right)' = \\frac{2}{7} \\cdot \\left(-\\frac{14}{3}\\right) \\cdot x^{-\\frac{17}{3}} -\\frac{3}{7} \\cdot \\mathrm{e}^x +\\frac{1}{2}\\cdot \\frac{1}{x} + 0 = -\\frac{4}{3} \\cdot x^{-\\frac{17}{3}} -\\frac{3}{7} \\cdot \\mathrm{e}^x +\\frac{1}{2}\\cdot \\frac{1}{x}$"], ["$f(x)=-\\frac{3}{7}\\cdot\\left(x^{\\frac{7}{4}} -\\frac{7}{6}\\cdot \\left(\\mathrm{e}^x -\\frac{2}{5}\\cdot \\ln(x)\\right) +\\frac{7}{9}\\right)$", "$f'(x) = \\left(-\\frac{3}{7}\\cdot x^{\\frac{7}{4}} + \\frac{1}{2}\\mathrm{e}^x +-\\frac{1}{5}\\ln(x) + -\\frac{1}{3}\\right)' = -\\frac{3}{7} \\cdot \\frac{7}{4} \\cdot x^{\\frac{3}{4}} +\\frac{1}{2} \\cdot \\mathrm{e}^x -\\frac{1}{5}\\cdot \\frac{1}{x} + 0 = -\\frac{3}{4} \\cdot x^{\\frac{3}{4}} +\\frac{1}{2} \\cdot \\mathrm{e}^x -\\frac{1}{5}\\cdot \\frac{1}{x}$"], ["$f(x)=-\\frac{2}{3}\\cdot\\left(x^{\\frac{2}{3}} +\\frac{3}{4}\\cdot \\left(\\mathrm{e}^x +\\frac{8}{7}\\cdot \\ln(x)\\right) -\\frac{1}{4}\\right)$", "$f'(x) = \\left(-\\frac{2}{3}\\cdot x^{\\frac{2}{3}} + -\\frac{1}{2}\\mathrm{e}^x +-\\frac{4}{7}\\ln(x) + \\frac{1}{6}\\right)' = -\\frac{2}{3} \\cdot \\frac{2}{3} \\cdot x^{-\\frac{1}{3}} -\\frac{1}{2} \\cdot \\mathrm{e}^x -\\frac{4}{7}\\cdot \\frac{1}{x} + 0 = -\\frac{4}{9} \\cdot x^{-\\frac{1}{3}} -\\frac{1}{2} \\cdot \\mathrm{e}^x -\\frac{4}{7}\\cdot \\frac{1}{x}$"]],
" <br><hr> ");
</JS>
<HTML>
<div id="exolincomb_exp_log_power"></div>

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