miniaufgabe.js
==== 25. März 2024 bis 29. März 2024 ====
=== Dienstag 26. März 2024 ===
Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren. Weitere Vereinfachungen sind nicht nötig.
miniAufgabe("#exoprod_ketten_nur_poly","#solprod_ketten_nur_poly",
[["$\\left(8x+8\\right)^{36} \\cdot \\left(3x^{6}+3\\right)^{27}$", "$$\\begin{multline*}\\left(\\left(8x+8\\right)^{36} \\cdot \\left(3x^{6}+3\\right)^{27}\\right)' = \\\\\n36\\cdot \\left(8x+8\\right)^{35}\\cdot \\left(8)\\right) \\cdot \\left(3x^{6}+3\\right)^{27} + \\left(8x+8\\right)^{36} \\cdot 27 \\cdot \\left(3x^{6}+3\\right)^{26} \\cdot \\left(18x^{5})\\right) = \\\\\n9 \\cdot \\left(8x+8\\right)^{35} \\cdot \\left(3x^{6}+3\\right)^{26} \\cdot \\left[ 4 \\cdot \\left(8\\right)\\cdot\\left(3x^{6}+3\\right) + 3 \\cdot \\left(8x+8\\right) \\cdot \\left(18x^{5}\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(-8x+11\\right)^{30} \\cdot \\left(4x^{4}+4x\\right)^{25}$", "$$\\begin{multline*}\\left(\\left(-8x+11\\right)^{30} \\cdot \\left(4x^{4}+4x\\right)^{25}\\right)' = \\\\\n30\\cdot \\left(-8x+11\\right)^{29}\\cdot \\left(-8)\\right) \\cdot \\left(4x^{4}+4x\\right)^{25} + \\left(-8x+11\\right)^{30} \\cdot 25 \\cdot \\left(4x^{4}+4x\\right)^{24} \\cdot \\left(16x^{3}+4)\\right) = \\\\\n5 \\cdot \\left(-8x+11\\right)^{29} \\cdot \\left(4x^{4}+4x\\right)^{24} \\cdot \\left[ 6 \\cdot \\left(-8\\right)\\cdot\\left(4x^{4}+4x\\right) + 5 \\cdot \\left(-8x+11\\right) \\cdot \\left(16x^{3}+4\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(-2x^{4}-2\\right)^{12} \\cdot \\left(9x-13\\right)^{42}$", "$$\\begin{multline*}\\left(\\left(-2x^{4}-2\\right)^{12} \\cdot \\left(9x-13\\right)^{42}\\right)' = \\\\\n12\\cdot \\left(-2x^{4}-2\\right)^{11}\\cdot \\left(-8x^{3})\\right) \\cdot \\left(9x-13\\right)^{42} + \\left(-2x^{4}-2\\right)^{12} \\cdot 42 \\cdot \\left(9x-13\\right)^{41} \\cdot \\left(9)\\right) = \\\\\n6 \\cdot \\left(-2x^{4}-2\\right)^{11} \\cdot \\left(9x-13\\right)^{41} \\cdot \\left[ 2 \\cdot \\left(-8x^{3}\\right)\\cdot\\left(9x-13\\right) + 7 \\cdot \\left(-2x^{4}-2\\right) \\cdot \\left(9\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(-7x^{6}-7x\\right)^{18} \\cdot \\left(7x-12\\right)^{27}$", "$$\\begin{multline*}\\left(\\left(-7x^{6}-7x\\right)^{18} \\cdot \\left(7x-12\\right)^{27}\\right)' = \\\\\n18\\cdot \\left(-7x^{6}-7x\\right)^{17}\\cdot \\left(-42x^{5}-7)\\right) \\cdot \\left(7x-12\\right)^{27} + \\left(-7x^{6}-7x\\right)^{18} \\cdot 27 \\cdot \\left(7x-12\\right)^{26} \\cdot \\left(7)\\right) = \\\\\n9 \\cdot \\left(-7x^{6}-7x\\right)^{17} \\cdot \\left(7x-12\\right)^{26} \\cdot \\left[ 2 \\cdot \\left(-42x^{5}-7\\right)\\cdot\\left(7x-12\\right) + 3 \\cdot \\left(-7x^{6}-7x\\right) \\cdot \\left(7\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(6x+7\\right)^{36} \\cdot \\left(4x^{4}-3\\right)^{8}$", "$$\\begin{multline*}\\left(\\left(6x+7\\right)^{36} \\cdot \\left(4x^{4}-3\\right)^{8}\\right)' = \\\\\n36\\cdot \\left(6x+7\\right)^{35}\\cdot \\left(6)\\right) \\cdot \\left(4x^{4}-3\\right)^{8} + \\left(6x+7\\right)^{36} \\cdot 8 \\cdot \\left(4x^{4}-3\\right)^{7} \\cdot \\left(16x^{3})\\right) = \\\\\n4 \\cdot \\left(6x+7\\right)^{35} \\cdot \\left(4x^{4}-3\\right)^{7} \\cdot \\left[ 9 \\cdot \\left(6\\right)\\cdot\\left(4x^{4}-3\\right) + 2 \\cdot \\left(6x+7\\right) \\cdot \\left(16x^{3}\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(-9x-4\\right)^{33} \\cdot \\left(7x^{4}-13x\\right)^{22}$", "$$\\begin{multline*}\\left(\\left(-9x-4\\right)^{33} \\cdot \\left(7x^{4}-13x\\right)^{22}\\right)' = \\\\\n33\\cdot \\left(-9x-4\\right)^{32}\\cdot \\left(-9)\\right) \\cdot \\left(7x^{4}-13x\\right)^{22} + \\left(-9x-4\\right)^{33} \\cdot 22 \\cdot \\left(7x^{4}-13x\\right)^{21} \\cdot \\left(28x^{3}-13)\\right) = \\\\\n11 \\cdot \\left(-9x-4\\right)^{32} \\cdot \\left(7x^{4}-13x\\right)^{21} \\cdot \\left[ 3 \\cdot \\left(-9\\right)\\cdot\\left(7x^{4}-13x\\right) + 2 \\cdot \\left(-9x-4\\right) \\cdot \\left(28x^{3}-13\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(10x+11\\right)^{28} \\cdot \\left(-9x^{5}-8x\\right)^{8}$", "$$\\begin{multline*}\\left(\\left(10x+11\\right)^{28} \\cdot \\left(-9x^{5}-8x\\right)^{8}\\right)' = \\\\\n28\\cdot \\left(10x+11\\right)^{27}\\cdot \\left(10)\\right) \\cdot \\left(-9x^{5}-8x\\right)^{8} + \\left(10x+11\\right)^{28} \\cdot 8 \\cdot \\left(-9x^{5}-8x\\right)^{7} \\cdot \\left(-45x^{4}-8)\\right) = \\\\\n4 \\cdot \\left(10x+11\\right)^{27} \\cdot \\left(-9x^{5}-8x\\right)^{7} \\cdot \\left[ 7 \\cdot \\left(10\\right)\\cdot\\left(-9x^{5}-8x\\right) + 2 \\cdot \\left(10x+11\\right) \\cdot \\left(-45x^{4}-8\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(7x^{5}-9x\\right)^{10} \\cdot \\left(-7x-4\\right)^{15}$", "$$\\begin{multline*}\\left(\\left(7x^{5}-9x\\right)^{10} \\cdot \\left(-7x-4\\right)^{15}\\right)' = \\\\\n10\\cdot \\left(7x^{5}-9x\\right)^{9}\\cdot \\left(35x^{4}-9)\\right) \\cdot \\left(-7x-4\\right)^{15} + \\left(7x^{5}-9x\\right)^{10} \\cdot 15 \\cdot \\left(-7x-4\\right)^{14} \\cdot \\left(-7)\\right) = \\\\\n5 \\cdot \\left(7x^{5}-9x\\right)^{9} \\cdot \\left(-7x-4\\right)^{14} \\cdot \\left[ 2 \\cdot \\left(35x^{4}-9\\right)\\cdot\\left(-7x-4\\right) + 3 \\cdot \\left(7x^{5}-9x\\right) \\cdot \\left(-7\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(7x^{4}-5\\right)^{10} \\cdot \\left(9x-2\\right)^{35}$", "$$\\begin{multline*}\\left(\\left(7x^{4}-5\\right)^{10} \\cdot \\left(9x-2\\right)^{35}\\right)' = \\\\\n10\\cdot \\left(7x^{4}-5\\right)^{9}\\cdot \\left(28x^{3})\\right) \\cdot \\left(9x-2\\right)^{35} + \\left(7x^{4}-5\\right)^{10} \\cdot 35 \\cdot \\left(9x-2\\right)^{34} \\cdot \\left(9)\\right) = \\\\\n5 \\cdot \\left(7x^{4}-5\\right)^{9} \\cdot \\left(9x-2\\right)^{34} \\cdot \\left[ 2 \\cdot \\left(28x^{3}\\right)\\cdot\\left(9x-2\\right) + 7 \\cdot \\left(7x^{4}-5\\right) \\cdot \\left(9\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(-12x+8\\right)^{42} \\cdot \\left(6x^{5}-12\\right)^{18}$", "$$\\begin{multline*}\\left(\\left(-12x+8\\right)^{42} \\cdot \\left(6x^{5}-12\\right)^{18}\\right)' = \\\\\n42\\cdot \\left(-12x+8\\right)^{41}\\cdot \\left(-12)\\right) \\cdot \\left(6x^{5}-12\\right)^{18} + \\left(-12x+8\\right)^{42} \\cdot 18 \\cdot \\left(6x^{5}-12\\right)^{17} \\cdot \\left(30x^{4})\\right) = \\\\\n6 \\cdot \\left(-12x+8\\right)^{41} \\cdot \\left(6x^{5}-12\\right)^{17} \\cdot \\left[ 7 \\cdot \\left(-12\\right)\\cdot\\left(6x^{5}-12\\right) + 3 \\cdot \\left(-12x+8\\right) \\cdot \\left(30x^{4}\\right) \\right] \\\\\n\\end{multline*}$$"]],
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ruby ableiten-von-hand.rb 12
=== Mittwoch 27. März 2024 ===
Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig.
miniAufgabe("#exoquotient_ketten_nur_poly","#solquotient_ketten_nur_poly",
[["$\\frac{ \\left(-2x^{5}+11x\\right)^{35} }{ \\left(7x-4\\right)^{21} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-2x^{5}+11x\\right)^{35} }{ \\left(7x-4\\right)^{21} }\\right)' = \\\\\n\\frac{ 35\\cdot \\left(-2x^{5}+11x\\right)^{34}\\cdot \\left(-10x^{4}+11)\\right) \\cdot \\left(7x-4\\right)^{21} - \\left(-2x^{5}+11x\\right)^{35} \\cdot 21 \\cdot \\left(7x-4\\right)^{20} \\cdot \\left(7)\\right) }{ \\left(\\left(7x-4\\right)^{21}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-2x^{5}+11x\\right)^{34} \\cdot \\left(7x-4\\right)^{20} \\cdot \\left[ 5 \\cdot \\left(-10x^{4}+11\\right) \\cdot \\left(7x-4\\right) - 3 \\cdot \\left(-2x^{5}+11x\\right) \\cdot \\left(7\\right) \\right] }{ \\left(7x-4\\right)^{42} }= \\\\\n\\frac{ 7 \\cdot \\left(-2x^{5}+11x\\right)^{34} \\cdot \\left[ 5 \\cdot \\left(-10x^{4}+11\\right) \\cdot \\left(7x-4\\right) - 3 \\cdot \\left(-2x^{5}+11x\\right) \\cdot \\left(7\\right) \\right] }{ \\left(7x-4\\right)^{22} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}-9x\\right)^{42} }{ \\left(-4x-2\\right)^{35} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}-9x\\right)^{42} }{ \\left(-4x-2\\right)^{35} }\\right)' = \\\\\n\\frac{ 42\\cdot \\left(2x^{4}-9x\\right)^{41}\\cdot \\left(8x^{3}-9)\\right) \\cdot \\left(-4x-2\\right)^{35} - \\left(2x^{4}-9x\\right)^{42} \\cdot 35 \\cdot \\left(-4x-2\\right)^{34} \\cdot \\left(-4)\\right) }{ \\left(\\left(-4x-2\\right)^{35}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(2x^{4}-9x\\right)^{41} \\cdot \\left(-4x-2\\right)^{34} \\cdot \\left[ 6 \\cdot \\left(8x^{3}-9\\right) \\cdot \\left(-4x-2\\right) - 5 \\cdot \\left(2x^{4}-9x\\right) \\cdot \\left(-4\\right) \\right] }{ \\left(-4x-2\\right)^{70} }= \\\\\n\\frac{ 7 \\cdot \\left(2x^{4}-9x\\right)^{41} \\cdot \\left[ 6 \\cdot \\left(8x^{3}-9\\right) \\cdot \\left(-4x-2\\right) - 5 \\cdot \\left(2x^{4}-9x\\right) \\cdot \\left(-4\\right) \\right] }{ \\left(-4x-2\\right)^{36} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-4x+11\\right)^{20} }{ \\left(-2x^{5}-13x\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-4x+11\\right)^{20} }{ \\left(-2x^{5}-13x\\right)^{28} }\\right)' = \\\\\n\\frac{ 20\\cdot \\left(-4x+11\\right)^{19}\\cdot \\left(-4)\\right) \\cdot \\left(-2x^{5}-13x\\right)^{28} - \\left(-4x+11\\right)^{20} \\cdot 28 \\cdot \\left(-2x^{5}-13x\\right)^{27} \\cdot \\left(-10x^{4}-13)\\right) }{ \\left(\\left(-2x^{5}-13x\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-4x+11\\right)^{19} \\cdot \\left(-2x^{5}-13x\\right)^{27} \\cdot \\left[ 5 \\cdot \\left(-4\\right) \\cdot \\left(-2x^{5}-13x\\right) - 7 \\cdot \\left(-4x+11\\right) \\cdot \\left(-10x^{4}-13\\right) \\right] }{ \\left(-2x^{5}-13x\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(-4x+11\\right)^{19} \\cdot \\left[ 5 \\cdot \\left(-4\\right) \\cdot \\left(-2x^{5}-13x\\right) - 7 \\cdot \\left(-4x+11\\right) \\cdot \\left(-10x^{4}-13\\right) \\right] }{ \\left(-2x^{5}-13x\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(3x+13\\right)^{12} }{ \\left(-2x^{5}+5\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(3x+13\\right)^{12} }{ \\left(-2x^{5}+5\\right)^{28} }\\right)' = \\\\\n\\frac{ 12\\cdot \\left(3x+13\\right)^{11}\\cdot \\left(3)\\right) \\cdot \\left(-2x^{5}+5\\right)^{28} - \\left(3x+13\\right)^{12} \\cdot 28 \\cdot \\left(-2x^{5}+5\\right)^{27} \\cdot \\left(-10x^{4})\\right) }{ \\left(\\left(-2x^{5}+5\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(3x+13\\right)^{11} \\cdot \\left(-2x^{5}+5\\right)^{27} \\cdot \\left[ 3 \\cdot \\left(3\\right) \\cdot \\left(-2x^{5}+5\\right) - 7 \\cdot \\left(3x+13\\right) \\cdot \\left(-10x^{4}\\right) \\right] }{ \\left(-2x^{5}+5\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(3x+13\\right)^{11} \\cdot \\left[ 3 \\cdot \\left(3\\right) \\cdot \\left(-2x^{5}+5\\right) - 7 \\cdot \\left(3x+13\\right) \\cdot \\left(-10x^{4}\\right) \\right] }{ \\left(-2x^{5}+5\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x-4\\right)^{21} }{ \\left(11x^{4}+7x\\right)^{14} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x-4\\right)^{21} }{ \\left(11x^{4}+7x\\right)^{14} }\\right)' = \\\\\n\\frac{ 21\\cdot \\left(-9x-4\\right)^{20}\\cdot \\left(-9)\\right) \\cdot \\left(11x^{4}+7x\\right)^{14} - \\left(-9x-4\\right)^{21} \\cdot 14 \\cdot \\left(11x^{4}+7x\\right)^{13} \\cdot \\left(44x^{3}+7)\\right) }{ \\left(\\left(11x^{4}+7x\\right)^{14}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-9x-4\\right)^{20} \\cdot \\left(11x^{4}+7x\\right)^{13} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(11x^{4}+7x\\right) - 2 \\cdot \\left(-9x-4\\right) \\cdot \\left(44x^{3}+7\\right) \\right] }{ \\left(11x^{4}+7x\\right)^{28} }= \\\\\n\\frac{ 7 \\cdot \\left(-9x-4\\right)^{20} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(11x^{4}+7x\\right) - 2 \\cdot \\left(-9x-4\\right) \\cdot \\left(44x^{3}+7\\right) \\right] }{ \\left(11x^{4}+7x\\right)^{15} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-2x^{5}-4\\right)^{24} }{ \\left(-12x+6\\right)^{36} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-2x^{5}-4\\right)^{24} }{ \\left(-12x+6\\right)^{36} }\\right)' = \\\\\n\\frac{ 24\\cdot \\left(-2x^{5}-4\\right)^{23}\\cdot \\left(-10x^{4})\\right) \\cdot \\left(-12x+6\\right)^{36} - \\left(-2x^{5}-4\\right)^{24} \\cdot 36 \\cdot \\left(-12x+6\\right)^{35} \\cdot \\left(-12)\\right) }{ \\left(\\left(-12x+6\\right)^{36}\\right)^2} = \\\\\n\\frac{ 12 \\cdot \\left(-2x^{5}-4\\right)^{23} \\cdot \\left(-12x+6\\right)^{35} \\cdot \\left[ 2 \\cdot \\left(-10x^{4}\\right) \\cdot \\left(-12x+6\\right) - 3 \\cdot \\left(-2x^{5}-4\\right) \\cdot \\left(-12\\right) \\right] }{ \\left(-12x+6\\right)^{72} }= \\\\\n\\frac{ 12 \\cdot \\left(-2x^{5}-4\\right)^{23} \\cdot \\left[ 2 \\cdot \\left(-10x^{4}\\right) \\cdot \\left(-12x+6\\right) - 3 \\cdot \\left(-2x^{5}-4\\right) \\cdot \\left(-12\\right) \\right] }{ \\left(-12x+6\\right)^{37} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(5x^{5}-7x\\right)^{16} }{ \\left(11x+3\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(5x^{5}-7x\\right)^{16} }{ \\left(11x+3\\right)^{24} }\\right)' = \\\\\n\\frac{ 16\\cdot \\left(5x^{5}-7x\\right)^{15}\\cdot \\left(25x^{4}-7)\\right) \\cdot \\left(11x+3\\right)^{24} - \\left(5x^{5}-7x\\right)^{16} \\cdot 24 \\cdot \\left(11x+3\\right)^{23} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+3\\right)^{24}\\right)^2} = \\\\\n\\frac{ 8 \\cdot \\left(5x^{5}-7x\\right)^{15} \\cdot \\left(11x+3\\right)^{23} \\cdot \\left[ 2 \\cdot \\left(25x^{4}-7\\right) \\cdot \\left(11x+3\\right) - 3 \\cdot \\left(5x^{5}-7x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+3\\right)^{48} }= \\\\\n\\frac{ 8 \\cdot \\left(5x^{5}-7x\\right)^{15} \\cdot \\left[ 2 \\cdot \\left(25x^{4}-7\\right) \\cdot \\left(11x+3\\right) - 3 \\cdot \\left(5x^{5}-7x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+3\\right)^{25} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+12\\right)^{26} }{ \\left(11x+4\\right)^{39} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+12\\right)^{26} }{ \\left(11x+4\\right)^{39} }\\right)' = \\\\\n\\frac{ 26\\cdot \\left(2x^{4}+12\\right)^{25}\\cdot \\left(8x^{3})\\right) \\cdot \\left(11x+4\\right)^{39} - \\left(2x^{4}+12\\right)^{26} \\cdot 39 \\cdot \\left(11x+4\\right)^{38} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+4\\right)^{39}\\right)^2} = \\\\\n\\frac{ 13 \\cdot \\left(2x^{4}+12\\right)^{25} \\cdot \\left(11x+4\\right)^{38} \\cdot \\left[ 2 \\cdot \\left(8x^{3}\\right) \\cdot \\left(11x+4\\right) - 3 \\cdot \\left(2x^{4}+12\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+4\\right)^{78} }= \\\\\n\\frac{ 13 \\cdot \\left(2x^{4}+12\\right)^{25} \\cdot \\left[ 2 \\cdot \\left(8x^{3}\\right) \\cdot \\left(11x+4\\right) - 3 \\cdot \\left(2x^{4}+12\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+4\\right)^{40} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(9x^{5}-3\\right)^{18} }{ \\left(4x^{5}-6x\\right)^{27} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(9x^{5}-3\\right)^{18} }{ \\left(4x^{5}-6x\\right)^{27} }\\right)' = \\\\\n\\frac{ 18\\cdot \\left(9x^{5}-3\\right)^{17}\\cdot \\left(45x^{4})\\right) \\cdot \\left(4x^{5}-6x\\right)^{27} - \\left(9x^{5}-3\\right)^{18} \\cdot 27 \\cdot \\left(4x^{5}-6x\\right)^{26} \\cdot \\left(20x^{4}-6)\\right) }{ \\left(\\left(4x^{5}-6x\\right)^{27}\\right)^2} = \\\\\n\\frac{ 9 \\cdot \\left(9x^{5}-3\\right)^{17} \\cdot \\left(4x^{5}-6x\\right)^{26} \\cdot \\left[ 2 \\cdot \\left(45x^{4}\\right) \\cdot \\left(4x^{5}-6x\\right) - 3 \\cdot \\left(9x^{5}-3\\right) \\cdot \\left(20x^{4}-6\\right) \\right] }{ \\left(4x^{5}-6x\\right)^{54} }= \\\\\n\\frac{ 9 \\cdot \\left(9x^{5}-3\\right)^{17} \\cdot \\left[ 2 \\cdot \\left(45x^{4}\\right) \\cdot \\left(4x^{5}-6x\\right) - 3 \\cdot \\left(9x^{5}-3\\right) \\cdot \\left(20x^{4}-6\\right) \\right] }{ \\left(4x^{5}-6x\\right)^{28} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(3x^{4}-5\\right)^{30} }{ \\left(8x-12\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(3x^{4}-5\\right)^{30} }{ \\left(8x-12\\right)^{24} }\\right)' = \\\\\n\\frac{ 30\\cdot \\left(3x^{4}-5\\right)^{29}\\cdot \\left(12x^{3})\\right) \\cdot \\left(8x-12\\right)^{24} - \\left(3x^{4}-5\\right)^{30} \\cdot 24 \\cdot \\left(8x-12\\right)^{23} \\cdot \\left(8)\\right) }{ \\left(\\left(8x-12\\right)^{24}\\right)^2} = \\\\\n\\frac{ 6 \\cdot \\left(3x^{4}-5\\right)^{29} \\cdot \\left(8x-12\\right)^{23} \\cdot \\left[ 5 \\cdot \\left(12x^{3}\\right) \\cdot \\left(8x-12\\right) - 4 \\cdot \\left(3x^{4}-5\\right) \\cdot \\left(8\\right) \\right] }{ \\left(8x-12\\right)^{48} }= \\\\\n\\frac{ 6 \\cdot \\left(3x^{4}-5\\right)^{29} \\cdot \\left[ 5 \\cdot \\left(12x^{3}\\right) \\cdot \\left(8x-12\\right) - 4 \\cdot \\left(3x^{4}-5\\right) \\cdot \\left(8\\right) \\right] }{ \\left(8x-12\\right)^{25} } \\\\\n\\end{multline*}$$"]],
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ruby ableiten-von-hand.rb 13