lehrkraefte:blc:miniaufgaben

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lehrkraefte:blc:miniaufgaben [2024/03/25 09:16]
Ivo Blöchliger
lehrkraefte:blc:miniaufgaben [2024/03/27 08:26] (current)
Ivo Blöchliger [25. März 2024 bis 29. März 2024]
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 === Mittwoch 27. März 2024 === === Mittwoch 27. März 2024 ===
-Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig.+Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus und kürzen Sie. Weitere Vereinfachungen sind nicht nötig.
 <JS>miniAufgabe("#exoquotient_ketten_nur_poly","#solquotient_ketten_nur_poly", <JS>miniAufgabe("#exoquotient_ketten_nur_poly","#solquotient_ketten_nur_poly",
 [["$\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }\\right)' = \\\\\n\\frac{ 36\\cdot \\left(-11x+7\\right)^{35}\\cdot \\left(-11)\\right) \\cdot \\left(-5x^{5}-2\\right)^{16} - \\left(-11x+7\\right)^{36} \\cdot 16 \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left(-25x^{4})\\right) }{ \\left(\\left(-5x^{5}-2\\right)^{16}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{32} }= \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{17} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(2x^{4}+7x\\right)^{27}\\cdot \\left(8x^{3}+7)\\right) \\cdot \\left(5x+3\\right)^{8} - \\left(2x^{4}+7x\\right)^{28} \\cdot 8 \\cdot \\left(5x+3\\right)^{7} \\cdot \\left(5)\\right) }{ \\left(\\left(5x+3\\right)^{8}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left(5x+3\\right)^{7} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{16} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{9} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }\\right)' = \\\\\n\\frac{ 39\\cdot \\left(-9x+12\\right)^{38}\\cdot \\left(-9)\\right) \\cdot \\left(-2x^{7}-12x\\right)^{26} - \\left(-9x+12\\right)^{39} \\cdot 26 \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left(-14x^{6}-12)\\right) }{ \\left(\\left(-2x^{7}-12x\\right)^{26}\\right)^2} = \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{52} }= \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{27} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(-5x+11\\right)^{27}\\cdot \\left(-5)\\right) \\cdot \\left(-2x^{5}+7x\\right)^{21} - \\left(-5x+11\\right)^{28} \\cdot 21 \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left(-10x^{4}+7)\\right) }{ \\left(\\left(-2x^{5}+7x\\right)^{21}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{42} }= \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{22} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(2x^{6}+5x\\right)^{7}\\cdot \\left(12x^{5}+5)\\right) \\cdot \\left(11x+9\\right)^{28} - \\left(2x^{6}+5x\\right)^{8} \\cdot 28 \\cdot \\left(11x+9\\right)^{27} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+9\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left(11x+9\\right)^{27} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(-5x-6\\right)^{7}\\cdot \\left(-5)\\right) \\cdot \\left(-5x^{5}-13x\\right)^{12} - \\left(-5x-6\\right)^{8} \\cdot 12 \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left(-25x^{4}-13)\\right) }{ \\left(\\left(-5x^{5}-13x\\right)^{12}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{24} }= \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{13} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }\\right)' = \\\\\n\\frac{ 20\\cdot \\left(-4x^{4}-3x\\right)^{19}\\cdot \\left(-16x^{3}-3)\\right) \\cdot \\left(3x+5\\right)^{24} - \\left(-4x^{4}-3x\\right)^{20} \\cdot 24 \\cdot \\left(3x+5\\right)^{23} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+5\\right)^{24}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left(3x+5\\right)^{23} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{48} }= \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{25} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }\\right)' = \\\\\n\\frac{ 40\\cdot \\left(2x^{4}+9x\\right)^{39}\\cdot \\left(8x^{3}+9)\\right) \\cdot \\left(3x+8\\right)^{30} - \\left(2x^{4}+9x\\right)^{40} \\cdot 30 \\cdot \\left(3x+8\\right)^{29} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+8\\right)^{30}\\right)^2} = \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left(3x+8\\right)^{29} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{60} }= \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{31} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }\\right)' = \\\\\n\\frac{ 16\\cdot \\left(-9x+10\\right)^{15}\\cdot \\left(-9)\\right) \\cdot \\left(2x^{7}+5x\\right)^{40} - \\left(-9x+10\\right)^{16} \\cdot 40 \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left(14x^{6}+5)\\right) }{ \\left(\\left(2x^{7}+5x\\right)^{40}\\right)^2} = \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{80} }= \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{41} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }\\right)' = \\\\\n\\frac{ 25\\cdot \\left(-13x+7\\right)^{24}\\cdot \\left(-13)\\right) \\cdot \\left(-2x^{7}-7\\right)^{10} - \\left(-13x+7\\right)^{25} \\cdot 10 \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left(-14x^{6})\\right) }{ \\left(\\left(-2x^{7}-7\\right)^{10}\\right)^2} = \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{20} }= \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{11} } \\\\\n\\end{multline*}$$"]], [["$\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }\\right)' = \\\\\n\\frac{ 36\\cdot \\left(-11x+7\\right)^{35}\\cdot \\left(-11)\\right) \\cdot \\left(-5x^{5}-2\\right)^{16} - \\left(-11x+7\\right)^{36} \\cdot 16 \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left(-25x^{4})\\right) }{ \\left(\\left(-5x^{5}-2\\right)^{16}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{32} }= \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{17} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(2x^{4}+7x\\right)^{27}\\cdot \\left(8x^{3}+7)\\right) \\cdot \\left(5x+3\\right)^{8} - \\left(2x^{4}+7x\\right)^{28} \\cdot 8 \\cdot \\left(5x+3\\right)^{7} \\cdot \\left(5)\\right) }{ \\left(\\left(5x+3\\right)^{8}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left(5x+3\\right)^{7} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{16} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{9} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }\\right)' = \\\\\n\\frac{ 39\\cdot \\left(-9x+12\\right)^{38}\\cdot \\left(-9)\\right) \\cdot \\left(-2x^{7}-12x\\right)^{26} - \\left(-9x+12\\right)^{39} \\cdot 26 \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left(-14x^{6}-12)\\right) }{ \\left(\\left(-2x^{7}-12x\\right)^{26}\\right)^2} = \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{52} }= \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{27} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(-5x+11\\right)^{27}\\cdot \\left(-5)\\right) \\cdot \\left(-2x^{5}+7x\\right)^{21} - \\left(-5x+11\\right)^{28} \\cdot 21 \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left(-10x^{4}+7)\\right) }{ \\left(\\left(-2x^{5}+7x\\right)^{21}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{42} }= \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{22} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(2x^{6}+5x\\right)^{7}\\cdot \\left(12x^{5}+5)\\right) \\cdot \\left(11x+9\\right)^{28} - \\left(2x^{6}+5x\\right)^{8} \\cdot 28 \\cdot \\left(11x+9\\right)^{27} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+9\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left(11x+9\\right)^{27} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(-5x-6\\right)^{7}\\cdot \\left(-5)\\right) \\cdot \\left(-5x^{5}-13x\\right)^{12} - \\left(-5x-6\\right)^{8} \\cdot 12 \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left(-25x^{4}-13)\\right) }{ \\left(\\left(-5x^{5}-13x\\right)^{12}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{24} }= \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{13} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }\\right)' = \\\\\n\\frac{ 20\\cdot \\left(-4x^{4}-3x\\right)^{19}\\cdot \\left(-16x^{3}-3)\\right) \\cdot \\left(3x+5\\right)^{24} - \\left(-4x^{4}-3x\\right)^{20} \\cdot 24 \\cdot \\left(3x+5\\right)^{23} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+5\\right)^{24}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left(3x+5\\right)^{23} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{48} }= \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{25} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }\\right)' = \\\\\n\\frac{ 40\\cdot \\left(2x^{4}+9x\\right)^{39}\\cdot \\left(8x^{3}+9)\\right) \\cdot \\left(3x+8\\right)^{30} - \\left(2x^{4}+9x\\right)^{40} \\cdot 30 \\cdot \\left(3x+8\\right)^{29} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+8\\right)^{30}\\right)^2} = \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left(3x+8\\right)^{29} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{60} }= \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{31} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }\\right)' = \\\\\n\\frac{ 16\\cdot \\left(-9x+10\\right)^{15}\\cdot \\left(-9)\\right) \\cdot \\left(2x^{7}+5x\\right)^{40} - \\left(-9x+10\\right)^{16} \\cdot 40 \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left(14x^{6}+5)\\right) }{ \\left(\\left(2x^{7}+5x\\right)^{40}\\right)^2} = \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{80} }= \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{41} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }\\right)' = \\\\\n\\frac{ 25\\cdot \\left(-13x+7\\right)^{24}\\cdot \\left(-13)\\right) \\cdot \\left(-2x^{7}-7\\right)^{10} - \\left(-13x+7\\right)^{25} \\cdot 10 \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left(-14x^{6})\\right) }{ \\left(\\left(-2x^{7}-7\\right)^{10}\\right)^2} = \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{20} }= \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{11} } \\\\\n\\end{multline*}$$"]],
  • lehrkraefte/blc/miniaufgaben.txt
  • Last modified: 2024/03/27 08:26
  • by Ivo Blöchliger