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This shows you the differences between two versions of the page.

--- lehrkraefte:blc:miniaufgaben [2024/03/25 09:16]
Ivo Blöchliger
+++ lehrkraefte:blc:miniaufgaben [2024/04/02 08:08]
Ivo Blöchliger
@@ Line 15: / Line 15: @@
-==== 25. März 2024 bis 29. März 2024 ====
+==== 1. April 2024 bis 5. April 2024 ====
-=== Dienstag 26. März 2024 ===
+=== Dienstag 2. April 2024 ===
-Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig.
+Keine Miniaufgbe. Frohe Ostern ;-)
-<JS>miniAufgabe("#exoprod_ketten_nur_poly","#solprod_ketten_nur_poly",
+=== Mittwoch 3. April 2024 ===
-[["$\\left(-3x-13\\right)^{25} \\cdot \\left(8x^{4}+7x\\right)^{10}$", "$$\\begin{multline*}\\left(\\left(-3x-13\\right)^{25} \\cdot \\left(8x^{4}+7x\\right)^{10}\\right)' = \\\\\n25\\cdot \\left(-3x-13\\right)^{24}\\cdot \\left(-3)\\right) \\cdot \\left(8x^{4}+7x\\right)^{10} + \\left(-3x-13\\right)^{25} \\cdot 10 \\cdot \\left(8x^{4}+7x\\right)^{9} \\cdot \\left(32x^{3}+7)\\right)  = \\\\\n5 \\cdot \\left(-3x-13\\right)^{24} \\cdot \\left(8x^{4}+7x\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-3\\right)\\cdot\\left(8x^{4}+7x\\right) + 2 \\cdot \\left(-3x-13\\right) \\cdot \\left(32x^{3}+7\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(9x-10\\right)^{20} \\cdot \\left(-3x^{4}-7x\\right)^{25}$", "$$\\begin{multline*}\\left(\\left(9x-10\\right)^{20} \\cdot \\left(-3x^{4}-7x\\right)^{25}\\right)' = \\\\\n20\\cdot \\left(9x-10\\right)^{19}\\cdot \\left(9)\\right) \\cdot \\left(-3x^{4}-7x\\right)^{25} + \\left(9x-10\\right)^{20} \\cdot 25 \\cdot \\left(-3x^{4}-7x\\right)^{24} \\cdot \\left(-12x^{3}-7)\\right)  = \\\\\n5 \\cdot \\left(9x-10\\right)^{19} \\cdot \\left(-3x^{4}-7x\\right)^{24} \\cdot \\left[ 4 \\cdot \\left(9\\right)\\cdot\\left(-3x^{4}-7x\\right) + 5 \\cdot \\left(9x-10\\right) \\cdot \\left(-12x^{3}-7\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(11x+9\\right)^{25} \\cdot \\left(8x^{4}-6x\\right)^{15}$", "$$\\begin{multline*}\\left(\\left(11x+9\\right)^{25} \\cdot \\left(8x^{4}-6x\\right)^{15}\\right)' = \\\\\n25\\cdot \\left(11x+9\\right)^{24}\\cdot \\left(11)\\right) \\cdot \\left(8x^{4}-6x\\right)^{15} + \\left(11x+9\\right)^{25} \\cdot 15 \\cdot \\left(8x^{4}-6x\\right)^{14} \\cdot \\left(32x^{3}-6)\\right)  = \\\\\n5 \\cdot \\left(11x+9\\right)^{24} \\cdot \\left(8x^{4}-6x\\right)^{14} \\cdot \\left[ 5 \\cdot \\left(11\\right)\\cdot\\left(8x^{4}-6x\\right) + 3 \\cdot \\left(11x+9\\right) \\cdot \\left(32x^{3}-6\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(3x^{7}+10x\\right)^{18} \\cdot \\left(7x+13\\right)^{27}$", "$$\\begin{multline*}\\left(\\left(3x^{7}+10x\\right)^{18} \\cdot \\left(7x+13\\right)^{27}\\right)' = \\\\\n18\\cdot \\left(3x^{7}+10x\\right)^{17}\\cdot \\left(21x^{6}+10)\\right) \\cdot \\left(7x+13\\right)^{27} + \\left(3x^{7}+10x\\right)^{18} \\cdot 27 \\cdot \\left(7x+13\\right)^{26} \\cdot \\left(7)\\right)  = \\\\\n9 \\cdot \\left(3x^{7}+10x\\right)^{17} \\cdot \\left(7x+13\\right)^{26} \\cdot \\left[ 2 \\cdot \\left(21x^{6}+10\\right)\\cdot\\left(7x+13\\right) + 3 \\cdot \\left(3x^{7}+10x\\right) \\cdot \\left(7\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(5x-5\\right)^{42} \\cdot \\left(4x^{7}+13x\\right)^{12}$", "$$\\begin{multline*}\\left(\\left(5x-5\\right)^{42} \\cdot \\left(4x^{7}+13x\\right)^{12}\\right)' = \\\\\n42\\cdot \\left(5x-5\\right)^{41}\\cdot \\left(5)\\right) \\cdot \\left(4x^{7}+13x\\right)^{12} + \\left(5x-5\\right)^{42} \\cdot 12 \\cdot \\left(4x^{7}+13x\\right)^{11} \\cdot \\left(28x^{6}+13)\\right)  = \\\\\n6 \\cdot \\left(5x-5\\right)^{41} \\cdot \\left(4x^{7}+13x\\right)^{11} \\cdot \\left[ 7 \\cdot \\left(5\\right)\\cdot\\left(4x^{7}+13x\\right) + 2 \\cdot \\left(5x-5\\right) \\cdot \\left(28x^{6}+13\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(8x^{6}-7x\\right)^{12} \\cdot \\left(-13x+7\\right)^{18}$", "$$\\begin{multline*}\\left(\\left(8x^{6}-7x\\right)^{12} \\cdot \\left(-13x+7\\right)^{18}\\right)' = \\\\\n12\\cdot \\left(8x^{6}-7x\\right)^{11}\\cdot \\left(48x^{5}-7)\\right) \\cdot \\left(-13x+7\\right)^{18} + \\left(8x^{6}-7x\\right)^{12} \\cdot 18 \\cdot \\left(-13x+7\\right)^{17} \\cdot \\left(-13)\\right)  = \\\\\n6 \\cdot \\left(8x^{6}-7x\\right)^{11} \\cdot \\left(-13x+7\\right)^{17} \\cdot \\left[ 2 \\cdot \\left(48x^{5}-7\\right)\\cdot\\left(-13x+7\\right) + 3 \\cdot \\left(8x^{6}-7x\\right) \\cdot \\left(-13\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(4x^{7}+11x\\right)^{15} \\cdot \\left(-4x+10\\right)^{10}$", "$$\\begin{multline*}\\left(\\left(4x^{7}+11x\\right)^{15} \\cdot \\left(-4x+10\\right)^{10}\\right)' = \\\\\n15\\cdot \\left(4x^{7}+11x\\right)^{14}\\cdot \\left(28x^{6}+11)\\right) \\cdot \\left(-4x+10\\right)^{10} + \\left(4x^{7}+11x\\right)^{15} \\cdot 10 \\cdot \\left(-4x+10\\right)^{9} \\cdot \\left(-4)\\right)  = \\\\\n5 \\cdot \\left(4x^{7}+11x\\right)^{14} \\cdot \\left(-4x+10\\right)^{9} \\cdot \\left[ 3 \\cdot \\left(28x^{6}+11\\right)\\cdot\\left(-4x+10\\right) + 2 \\cdot \\left(4x^{7}+11x\\right) \\cdot \\left(-4\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(5x^{5}+4\\right)^{28} \\cdot \\left(-13x-9\\right)^{21}$", "$$\\begin{multline*}\\left(\\left(5x^{5}+4\\right)^{28} \\cdot \\left(-13x-9\\right)^{21}\\right)' = \\\\\n28\\cdot \\left(5x^{5}+4\\right)^{27}\\cdot \\left(25x^{4})\\right) \\cdot \\left(-13x-9\\right)^{21} + \\left(5x^{5}+4\\right)^{28} \\cdot 21 \\cdot \\left(-13x-9\\right)^{20} \\cdot \\left(-13)\\right)  = \\\\\n7 \\cdot \\left(5x^{5}+4\\right)^{27} \\cdot \\left(-13x-9\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(25x^{4}\\right)\\cdot\\left(-13x-9\\right) + 3 \\cdot \\left(5x^{5}+4\\right) \\cdot \\left(-13\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(2x^{4}-13\\right)^{40} \\cdot \\left(-13x+12\\right)^{15}$", "$$\\begin{multline*}\\left(\\left(2x^{4}-13\\right)^{40} \\cdot \\left(-13x+12\\right)^{15}\\right)' = \\\\\n40\\cdot \\left(2x^{4}-13\\right)^{39}\\cdot \\left(8x^{3})\\right) \\cdot \\left(-13x+12\\right)^{15} + \\left(2x^{4}-13\\right)^{40} \\cdot 15 \\cdot \\left(-13x+12\\right)^{14} \\cdot \\left(-13)\\right)  = \\\\\n5 \\cdot \\left(2x^{4}-13\\right)^{39} \\cdot \\left(-13x+12\\right)^{14} \\cdot \\left[ 8 \\cdot \\left(8x^{3}\\right)\\cdot\\left(-13x+12\\right) + 3 \\cdot \\left(2x^{4}-13\\right) \\cdot \\left(-13\\right) \\right]  \\\\\n\\end{multline*}$$"], ["$\\left(3x^{5}-11\\right)^{12} \\cdot \\left(11x+3\\right)^{32}$", "$$\\begin{multline*}\\left(\\left(3x^{5}-11\\right)^{12} \\cdot \\left(11x+3\\right)^{32}\\right)' = \\\\\n12\\cdot \\left(3x^{5}-11\\right)^{11}\\cdot \\left(15x^{4})\\right) \\cdot \\left(11x+3\\right)^{32} + \\left(3x^{5}-11\\right)^{12} \\cdot 32 \\cdot \\left(11x+3\\right)^{31} \\cdot \\left(11)\\right)  = \\\\\n4 \\cdot \\left(3x^{5}-11\\right)^{11} \\cdot \\left(11x+3\\right)^{31} \\cdot \\left[ 3 \\cdot \\left(15x^{4}\\right)\\cdot\\left(11x+3\\right) + 8 \\cdot \\left(3x^{5}-11\\right) \\cdot \\left(11\\right) \\right]  \\\\\n\\end{multline*}$$"]],
+Prüfung, keine Miniaufgabe.
-" <br><hr> ");
-</JS>
-<HTML>
-<div id="exoprod_ketten_nur_poly"></div>
-</HTML>
-<hidden Lösungen>
-<HTML>
-<div id="solprod_ketten_nur_poly"></div>
-<div style='font-size:12px;color:gray;'>ruby ableiten-von-hand.rb 12</div>
-</HTML>
-</hidden>
-=== Mittwoch 27. März 2024 ===
-Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig.
-<JS>miniAufgabe("#exoquotient_ketten_nur_poly","#solquotient_ketten_nur_poly",
-[["$\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }\\right)' = \\\\\n\\frac{ 36\\cdot \\left(-11x+7\\right)^{35}\\cdot \\left(-11)\\right) \\cdot \\left(-5x^{5}-2\\right)^{16} - \\left(-11x+7\\right)^{36} \\cdot 16 \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left(-25x^{4})\\right) }{ \\left(\\left(-5x^{5}-2\\right)^{16}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{32} }= \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{17} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(2x^{4}+7x\\right)^{27}\\cdot \\left(8x^{3}+7)\\right) \\cdot \\left(5x+3\\right)^{8} - \\left(2x^{4}+7x\\right)^{28} \\cdot 8 \\cdot \\left(5x+3\\right)^{7} \\cdot \\left(5)\\right) }{ \\left(\\left(5x+3\\right)^{8}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left(5x+3\\right)^{7} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{16} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{9} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }\\right)' = \\\\\n\\frac{ 39\\cdot \\left(-9x+12\\right)^{38}\\cdot \\left(-9)\\right) \\cdot \\left(-2x^{7}-12x\\right)^{26} - \\left(-9x+12\\right)^{39} \\cdot 26 \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left(-14x^{6}-12)\\right) }{ \\left(\\left(-2x^{7}-12x\\right)^{26}\\right)^2} = \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{52} }= \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{27} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(-5x+11\\right)^{27}\\cdot \\left(-5)\\right) \\cdot \\left(-2x^{5}+7x\\right)^{21} - \\left(-5x+11\\right)^{28} \\cdot 21 \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left(-10x^{4}+7)\\right) }{ \\left(\\left(-2x^{5}+7x\\right)^{21}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{42} }= \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{22} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(2x^{6}+5x\\right)^{7}\\cdot \\left(12x^{5}+5)\\right) \\cdot \\left(11x+9\\right)^{28} - \\left(2x^{6}+5x\\right)^{8} \\cdot 28 \\cdot \\left(11x+9\\right)^{27} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+9\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left(11x+9\\right)^{27} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(-5x-6\\right)^{7}\\cdot \\left(-5)\\right) \\cdot \\left(-5x^{5}-13x\\right)^{12} - \\left(-5x-6\\right)^{8} \\cdot 12 \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left(-25x^{4}-13)\\right) }{ \\left(\\left(-5x^{5}-13x\\right)^{12}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{24} }= \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{13} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }\\right)' = \\\\\n\\frac{ 20\\cdot \\left(-4x^{4}-3x\\right)^{19}\\cdot \\left(-16x^{3}-3)\\right) \\cdot \\left(3x+5\\right)^{24} - \\left(-4x^{4}-3x\\right)^{20} \\cdot 24 \\cdot \\left(3x+5\\right)^{23} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+5\\right)^{24}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left(3x+5\\right)^{23} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{48} }= \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{25} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }\\right)' = \\\\\n\\frac{ 40\\cdot \\left(2x^{4}+9x\\right)^{39}\\cdot \\left(8x^{3}+9)\\right) \\cdot \\left(3x+8\\right)^{30} - \\left(2x^{4}+9x\\right)^{40} \\cdot 30 \\cdot \\left(3x+8\\right)^{29} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+8\\right)^{30}\\right)^2} = \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left(3x+8\\right)^{29} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{60} }= \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{31} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }\\right)' = \\\\\n\\frac{ 16\\cdot \\left(-9x+10\\right)^{15}\\cdot \\left(-9)\\right) \\cdot \\left(2x^{7}+5x\\right)^{40} - \\left(-9x+10\\right)^{16} \\cdot 40 \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left(14x^{6}+5)\\right) }{ \\left(\\left(2x^{7}+5x\\right)^{40}\\right)^2} = \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{80} }= \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{41} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }\\right)' = \\\\\n\\frac{ 25\\cdot \\left(-13x+7\\right)^{24}\\cdot \\left(-13)\\right) \\cdot \\left(-2x^{7}-7\\right)^{10} - \\left(-13x+7\\right)^{25} \\cdot 10 \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left(-14x^{6})\\right) }{ \\left(\\left(-2x^{7}-7\\right)^{10}\\right)^2} = \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{20} }= \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{11} } \\\\\n\\end{multline*}$$"]],
-" <br><hr> ");
-</JS>
-<HTML>
-<div id="exoquotient_ketten_nur_poly"></div>
-</HTML>
-<hidden Lösungen>
-<HTML>
-<div id="solquotient_ketten_nur_poly"></div>
-<div style='font-size:12px;color:gray;'>ruby ableiten-von-hand.rb 13</div>
-</HTML>
-</hidden>
 ==== Aufgaben vom aktuellen Jahr ====
   * [[lehrkraefte:blc:miniaufgaben:kw13-2024|KW13, 25. März 2024: Produkt- und Kettenregel auf Polynomterme anweden. Quotienten- und Kettenregel auf Polynomterme anweden.]]