miniaufgabe.js ==== 9. September 2019 bis 13. September 2019 ==== === Dienstag 10. September 2019 === Schreiben Sie die Funktion $k(x)$ als Verknüpfung zweier nicht-trivialer Funktionen $f(x)$ und $g(x)$. (Eine triviale Funktion wäre $f(x)=x$): miniAufgabe("#exofunktionenentschachteln","#solfunktionenentschachteln", [["$k(x)=\\mathrm{e}^{x^4}$", "$f(x)=\\mathrm{e}^x,\\quad g(x)=x^4$"], ["$k(x)={\\mathrm{e}^x}^4}$", "$f(x)=x^4,\\quad g(x)=\\mathrm{e}^x$"], ["$k(x)=\\ln\\left(x^5+x^4\\right)$", "$f(x)=\\ln(x),\\quad g(x)=x^5+x^4$"], ["$k(x)=\\left(\\ln(x)\\right)^4$", "$$f(x)=x^4,\\quad g(x)=\\ln(x)$"], ["$k(x)=\\sqrt{\\ln(x)}$", "$f(x)=\\sqrt{x},\\quad g(x)=\\ln(x)$"], ["$k(x)=\\mathrm{e}^{\\sqrt{x}}$", "$f(x)=\\mathrm{e}^x,\\quad g(x)=\\sqrt{x}$"], ["$k(x)=\\ln\\left(\\sqrt{x}\\right)$", "$f(x)=\\ln(x),\\quad g(x)=\\sqrt{x}$"], ["$k(x)=\\mathrm{e}^{\\mathrm{e}^x}$", "$f(x)=\\mathrm{e}^x,\\quad g(x)=\\mathrm{e}^x$"], ["$k(x)=\\ln(\\ln(x))$", "$f(x)=\\ln(x),\\quad g(x)=\\ln(x)$"], ["$k(x)=\\sqrt{\\sqrt{x}}$", "$f(x)=\\sqrt{x},\\quad g(x)=\\sqrt{x}$"], ["$k(x)=\\left(x^4+1\\right)^9$", "$f(x)=x^9,\\quad g(x)=x^4+1$"]], " $\\qquad$ ", " $\\qquad$ ", 3);});

=== Donnerstag 12. September 2019 === Leiten Sie von Hand und ohne Unterlagen ab: miniAufgabe("#exokettenregelvonpoly","#solkettenregelvonpoly", [["a) $f(x)=\\ln\\left(\\frac{3}{8}x^{4}-\\frac{2}{7}x^{3}-\\frac{3}{5}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(-\\frac{2}{3}x^{4}+\\frac{1}{2}x^{3}-\\frac{2}{7}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{\\frac{3}{8}x^{4}-\\frac{2}{7}x^{3}-\\frac{3}{5}}\\cdot \\left(\\frac{3}{2}x^{3}-\\frac{6}{7}x^{2}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(-\\frac{2}{3}x^{4}+\\frac{1}{2}x^{3}-\\frac{2}{7}\\right)}\\cdot \\left(-\\frac{8}{3}x^{3}+\\frac{3}{2}x^{2}\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(\\frac{1}{4}x^{3}-\\frac{2}{9}x^{2}-\\frac{1}{7}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(\\frac{3}{8}x^{3}+\\frac{3}{7}x^{2}-\\frac{2}{3}x\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{\\frac{1}{4}x^{3}-\\frac{2}{9}x^{2}-\\frac{1}{7}}\\cdot \\left(\\frac{3}{4}x^{2}-\\frac{4}{9}x\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(\\frac{3}{8}x^{3}+\\frac{3}{7}x^{2}-\\frac{2}{3}x\\right)}\\cdot \\left(\\frac{9}{8}x^{2}+\\frac{6}{7}x-\\frac{2}{3}\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(-\\frac{4}{9}x^{4}+\\frac{3}{8}x^{2}-\\frac{1}{2}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(-\\frac{1}{8}x^{4}+\\frac{4}{5}x^{3}+\\frac{4}{9}x\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{-\\frac{4}{9}x^{4}+\\frac{3}{8}x^{2}-\\frac{1}{2}}\\cdot \\left(-\\frac{16}{9}x^{3}+\\frac{3}{4}x\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(-\\frac{1}{8}x^{4}+\\frac{4}{5}x^{3}+\\frac{4}{9}x\\right)}\\cdot \\left(-\\frac{1}{2}x^{3}+\\frac{12}{5}x^{2}+\\frac{4}{9}\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(\\frac{4}{5}x^{3}-\\frac{3}{2}x^{2}+\\frac{2}{5}x\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(-\\frac{4}{5}x^{2}-\\frac{2}{3}x+\\frac{1}{6}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{\\frac{4}{5}x^{3}-\\frac{3}{2}x^{2}+\\frac{2}{5}x}\\cdot \\left(\\frac{12}{5}x^{2}-3x+\\frac{2}{5}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(-\\frac{4}{5}x^{2}-\\frac{2}{3}x+\\frac{1}{6}\\right)}\\cdot \\left(-\\frac{8}{5}x-\\frac{2}{3}\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(-\\frac{3}{4}x^{3}-\\frac{3}{2}x^{2}-\\frac{4}{5}x\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(\\frac{2}{9}x^{3}+\\frac{1}{2}x^{2}-\\frac{1}{8}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{-\\frac{3}{4}x^{3}-\\frac{3}{2}x^{2}-\\frac{4}{5}x}\\cdot \\left(-\\frac{9}{4}x^{2}-3x-\\frac{4}{5}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(\\frac{2}{9}x^{3}+\\frac{1}{2}x^{2}-\\frac{1}{8}\\right)}\\cdot \\left(\\frac{2}{3}x^{2}+x\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(\\frac{2}{3}x^{4}-\\frac{4}{7}x^{3}+\\frac{4}{5}x^{2}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(\\frac{3}{8}x^{4}-\\frac{2}{9}x^{2}+\\frac{3}{8}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{\\frac{2}{3}x^{4}-\\frac{4}{7}x^{3}+\\frac{4}{5}x^{2}}\\cdot \\left(\\frac{8}{3}x^{3}-\\frac{12}{7}x^{2}+\\frac{8}{5}x\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(\\frac{3}{8}x^{4}-\\frac{2}{9}x^{2}+\\frac{3}{8}\\right)}\\cdot \\left(\\frac{3}{2}x^{3}-\\frac{4}{9}x\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(-\\frac{4}{3}x^{2}-\\frac{2}{3}x+\\frac{2}{3}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(\\frac{4}{3}x^{4}-\\frac{3}{2}x^{3}+\\frac{1}{2}x^{2}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{-\\frac{4}{3}x^{2}-\\frac{2}{3}x+\\frac{2}{3}}\\cdot \\left(-\\frac{8}{3}x-\\frac{2}{3}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(\\frac{4}{3}x^{4}-\\frac{3}{2}x^{3}+\\frac{1}{2}x^{2}\\right)}\\cdot \\left(\\frac{16}{3}x^{3}-\\frac{9}{2}x^{2}+x\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(-\\frac{1}{3}x^{4}+\\frac{2}{5}x^{3}+\\frac{1}{3}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(-\\frac{1}{2}x^{3}+\\frac{1}{2}x^{2}+\\frac{3}{2}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{-\\frac{1}{3}x^{4}+\\frac{2}{5}x^{3}+\\frac{1}{3}}\\cdot \\left(-\\frac{4}{3}x^{3}+\\frac{6}{5}x^{2}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(-\\frac{1}{2}x^{3}+\\frac{1}{2}x^{2}+\\frac{3}{2}\\right)}\\cdot \\left(-\\frac{3}{2}x^{2}+x\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(\\frac{3}{5}x^{4}+\\frac{1}{4}x^{2}-\\frac{1}{3}x\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(\\frac{2}{9}x^{2}+\\frac{1}{4}x+\\frac{1}{3}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{\\frac{3}{5}x^{4}+\\frac{1}{4}x^{2}-\\frac{1}{3}x}\\cdot \\left(\\frac{12}{5}x^{3}+\\frac{1}{2}x-\\frac{1}{3}\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(\\frac{2}{9}x^{2}+\\frac{1}{4}x+\\frac{1}{3}\\right)}\\cdot \\left(\\frac{4}{9}x+\\frac{1}{4}\\right)\\quad$ "], ["a) $f(x)=\\ln\\left(-\\frac{1}{3}x^{3}+\\frac{1}{4}x^{2}-\\frac{3}{2}\\right)\\quad$ b) $f(x)=\\mathrm{e}^{\\left(-\\frac{3}{4}x^{4}-\\frac{1}{7}x+\\frac{1}{5}\\right)}\\quad$ ", "a) $f'(x)=\\frac{1}{-\\frac{1}{3}x^{3}+\\frac{1}{4}x^{2}-\\frac{3}{2}}\\cdot \\left(-x^{2}+\\frac{1}{2}x\\right)\\quad$ b) $f'(x)=\\mathrm{e}^{\\left(-\\frac{3}{4}x^{4}-\\frac{1}{7}x+\\frac{1}{5}\\right)}\\cdot \\left(-3x^{3}-\\frac{1}{7}\\right)\\quad$ "]], "
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