miniaufgabe.js ==== 14. Mai 2018 bis 18. Mai 2018 ==== === Dienstag 15. Mai 2018 === Leiten Sie von Hand und ohne Unterlagen ab: miniAufgabe("#exoableiten","#solableiten", [["a) $f(x)=-\\frac{1}{2}x^{9}+\\frac{4}{3}x^{4}+\\frac{1}{6}x^{3}\\quad$ b) $f(x)=-\\frac{4}{9}\\ln(x)\\quad$ c) $f(x)=\\frac{3}{4}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{1}{5}\\cdot 5^{x}\\quad$ ", "a) $f'(x)=-\\frac{9}{2}x^{8}+\\frac{16}{3}x^{3}+\\frac{1}{2}x^{2}\\quad$ b) $f'(x)=-\\frac{4}{9}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{3}{8}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{1}{5}\\cdot \\ln(5) \\cdot 5^x\\quad$ "], ["a) $f(x)=\\frac{2}{7}x^{12}+\\frac{1}{9}x^{8}+\\frac{2}{9}x^{2}\\quad$ b) $f(x)=-\\frac{1}{4}\\ln(x)\\quad$ c) $f(x)=\\frac{2}{7}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{2}{3}\\cdot 3^{x}\\quad$ ", "a) $f'(x)=\\frac{24}{7}x^{11}+\\frac{8}{9}x^{7}+\\frac{4}{9}x^{1}\\quad$ b) $f'(x)=-\\frac{1}{4}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{1}{7}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{2}{3}\\cdot \\ln(3) \\cdot 3^x\\quad$ "], ["a) $f(x)=\\frac{3}{2}x^{11}+\\frac{3}{4}x^{8}+\\frac{1}{2}x^{4}\\quad$ b) $f(x)=\\frac{3}{7}\\ln(x)\\quad$ c) $f(x)=\\frac{2}{5}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{1}{2}\\cdot 2^{x}\\quad$ ", "a) $f'(x)=\\frac{33}{2}x^{10}+6x^{7}+2x^{3}\\quad$ b) $f'(x)=\\frac{3}{7}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{1}{5}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{1}{2}\\cdot \\ln(2) \\cdot 2^x\\quad$ "], ["a) $f(x)=\\frac{1}{3}x^{10}+\\frac{1}{2}x^{9}+\\frac{1}{2}x^{7}\\quad$ b) $f(x)=\\frac{3}{8}\\ln(x)\\quad$ c) $f(x)=-\\frac{4}{9}\\cdot \\sqrt{x}\\quad$ d) $f(x)=-\\frac{3}{7}\\cdot 4^{x}\\quad$ ", "a) $f'(x)=\\frac{10}{3}x^{9}+\\frac{9}{2}x^{8}+\\frac{7}{2}x^{6}\\quad$ b) $f'(x)=\\frac{3}{8}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=-\\frac{2}{9}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=-\\frac{3}{7}\\cdot \\ln(4) \\cdot 4^x\\quad$ "], ["a) $f(x)=\\frac{1}{8}x^{12}+\\frac{1}{6}x^{11}+\\frac{1}{8}x^{4}\\quad$ b) $f(x)=\\frac{1}{4}\\ln(x)\\quad$ c) $f(x)=\\frac{3}{7}\\cdot \\sqrt{x}\\quad$ d) $f(x)=-\\frac{3}{2}\\cdot 4^{x}\\quad$ ", "a) $f'(x)=\\frac{3}{2}x^{11}+\\frac{11}{6}x^{10}+\\frac{1}{2}x^{3}\\quad$ b) $f'(x)=\\frac{1}{4}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{3}{14}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=-\\frac{3}{2}\\cdot \\ln(4) \\cdot 4^x\\quad$ "], ["a) $f(x)=-\\frac{3}{8}x^{10}-\\frac{1}{3}x^{3}-\\frac{2}{5}x^{2}\\quad$ b) $f(x)=-\\frac{1}{2}\\ln(x)\\quad$ c) $f(x)=-\\frac{3}{5}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{4}{7}\\cdot 3^{x}\\quad$ ", "a) $f'(x)=-\\frac{15}{4}x^{9}-1x^{2}-\\frac{4}{5}x^{1}\\quad$ b) $f'(x)=-\\frac{1}{2}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=-\\frac{3}{10}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{4}{7}\\cdot \\ln(3) \\cdot 3^x\\quad$ "], ["a) $f(x)=\\frac{3}{5}x^{11}+\\frac{1}{7}x^{10}+\\frac{4}{5}x^{6}\\quad$ b) $f(x)=-\\frac{1}{3}\\ln(x)\\quad$ c) $f(x)=-\\frac{1}{3}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{1}{2}\\cdot 4^{x}\\quad$ ", "a) $f'(x)=\\frac{33}{5}x^{10}+\\frac{10}{7}x^{9}+\\frac{24}{5}x^{5}\\quad$ b) $f'(x)=-\\frac{1}{3}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=-\\frac{1}{6}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{1}{2}\\cdot \\ln(4) \\cdot 4^x\\quad$ "], ["a) $f(x)=-\\frac{3}{4}x^{10}+\\frac{1}{2}x^{7}+\\frac{4}{5}x^{5}\\quad$ b) $f(x)=-\\frac{1}{4}\\ln(x)\\quad$ c) $f(x)=\\frac{1}{3}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{1}{3}\\cdot 3^{x}\\quad$ ", "a) $f'(x)=-\\frac{15}{2}x^{9}+\\frac{7}{2}x^{6}+4x^{4}\\quad$ b) $f'(x)=-\\frac{1}{4}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{1}{6}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{1}{3}\\cdot \\ln(3) \\cdot 3^x\\quad$ "], ["a) $f(x)=-\\frac{3}{4}x^{7}-\\frac{2}{3}x^{4}+\\frac{1}{4}x^{2}\\quad$ b) $f(x)=-\\frac{2}{9}\\ln(x)\\quad$ c) $f(x)=-\\frac{1}{2}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{3}{5}\\cdot 2^{x}\\quad$ ", "a) $f'(x)=-\\frac{21}{4}x^{6}-\\frac{8}{3}x^{3}+\\frac{1}{2}x^{1}\\quad$ b) $f'(x)=-\\frac{2}{9}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=-\\frac{1}{4}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{3}{5}\\cdot \\ln(2) \\cdot 2^x\\quad$ "], ["a) $f(x)=-\\frac{1}{4}x^{12}-\\frac{1}{2}x^{11}-\\frac{2}{3}x^{8}\\quad$ b) $f(x)=\\frac{1}{4}\\ln(x)\\quad$ c) $f(x)=\\frac{2}{7}\\cdot \\sqrt{x}\\quad$ d) $f(x)=\\frac{3}{2}\\cdot 3^{x}\\quad$ ", "a) $f'(x)=-3x^{11}-\\frac{11}{2}x^{10}-\\frac{16}{3}x^{7}\\quad$ b) $f'(x)=\\frac{1}{4}\\cdot \\frac{1}{x}\\quad$ c) $f'(x)=\\frac{1}{7}\\cdot \\frac{1}{\\sqrt{x}}\\quad$ d) $f'(x)=\\frac{3}{2}\\cdot \\ln(3) \\cdot 3^x\\quad$ "]], "
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=== Freitag 18. Mai 2018 === Vereinfachen Sie und schreiben Sie als eine Potenz von $x$ miniAufgabe("#exobruchexp","#solbruchexp", [["$\\left(x^{\\frac{6}{5}}\\right)^{\\frac{65}{36}}: x^{\\frac{5}{3}}$", "$x^{\\frac{1}{2}}$"], ["$\\left(x^{\\frac{4}{5}}\\cdot x^{\\frac{9}{2}}\\right)^{-\\frac{50}{159}}$", "$x^{-\\frac{5}{3}}$"], ["$\\left(x^{\\frac{6}{5}}\\cdot x^{\\frac{5}{6}}\\right)^{\\frac{18}{61}}$", "$x^{\\frac{3}{5}}$"], ["$\\left(x^{\\frac{4}{3}}: x^{\\frac{3}{2}}\\right)^{-\\frac{24}{5}}$", "$x^{\\frac{4}{5}}$"], ["$\\left(x^{\\frac{3}{2}}\\cdot x^{\\frac{9}{4}}\\right)^{-\\frac{14}{15}}$", "$x^{-\\frac{7}{2}}$"], ["$\\left(x^{\\frac{6}{5}}\\cdot x^{\\frac{5}{6}}\\right)^{-\\frac{135}{61}}$", "$x^{-\\frac{9}{2}}$"], ["$\\left(x^{\\frac{7}{6}}: x^{\\frac{3}{5}}\\right)^{-\\frac{45}{34}}$", "$x^{-\\frac{3}{4}}$"], ["$\\left(x^{\\frac{8}{3}}\\right)^{\\frac{35}{32}}: x^{\\frac{2}{3}}$", "$x^{\\frac{9}{4}}$"], ["$\\left(x^{\\frac{1}{2}}\\cdot x^{\\frac{3}{4}}\\right)^{-\\frac{36}{25}}$", "$x^{-\\frac{9}{5}}$"], ["$\\left(x^{\\frac{7}{4}}\\cdot x^{\\frac{1}{2}}\\right)^{-\\frac{8}{27}}$", "$x^{-\\frac{2}{3}}$"]], "     ");