From e14a9a0d1995d5c47ab87f1e221b7f5010f0a3d4 Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Mon, 18 Nov 2024 12:12:46 +0100 Subject: [PATCH] Mathe am 18.11.2024 --- schule/mathe/MA_2024-11-18.typ | 80 ++++++++++++++++++++++++++++ schule/mathe/pdfs/MA_2024-11-18.pdf | Bin 0 -> 29531 bytes 2 files changed, 80 insertions(+) create mode 100644 schule/mathe/MA_2024-11-18.typ create mode 100644 schule/mathe/pdfs/MA_2024-11-18.pdf diff --git a/schule/mathe/MA_2024-11-18.typ b/schule/mathe/MA_2024-11-18.typ new file mode 100644 index 0000000..b080672 --- /dev/null +++ b/schule/mathe/MA_2024-11-18.typ @@ -0,0 +1,80 @@ +#import "@preview/grape-suite:1.0.0": exercise +#import exercise: project, task, subtask + +#set text(lang: "de") + +#show: project.with( + title: [Kettenregel], + seminar: [Mathe Q2], + show-outline: true, + author: "Erik Grobecker", + date: datetime(day: 18, month: 11, year: 2024), + show-solutions: false, +) + +#show heading.where(level: 1): it => { + counter(math.equation).update(0) + it +} + +#show math.equation: set text(font: "New Computer Modern Math") + += Kettenregel + +$ + f(x)&= underbrace((3/4 x^2 -3), u) dot underbrace(e^(1.4-x^2), v) \ + f'(x)&=u' dot v + u dot v'\ + + u'&=3/4 dot 2x^1\ & + = 3/2 dot x\ + + v'&=e^(1.4-x^2)\ + &=e^(overbrace(1.4-x^2, "innere Ableitung")) \ + &=e^(1.4-x^2) dot overbrace((-2x), "innere Ableitung")\ + \ + "Einsetzen:"\ + f'(x)&=u' dot v + u dot v'\ + &=3/2x dot e^(1.4-x^2) + (3/4 x^2 -3) dot e^(1.4-x^2) dot (-2x) #h(2em)&| e "entfernen" \ + &=e^(1.4-x^2) dot (3/2x + (3/4x^2-3) dot (-2x))\ + &=e^(1.4-x^2) dot (3/2x -3/2x^3 + 6x)\ + &=e^(1.4-x^2) dot (-3/2x^3 + 15/2x) +$ + +Innere Ableitung: +$ + u(x)&=1.4-x^2\ + u'(x)&=2x +$ + +#pagebreak() + +== Aufgabe +Leite die folgenden Funktionen ab: + +*1)* +$ + f(x)&=e^(2x)\ + f'(x)&=e^(2x)dot 2\ + &=2e^(2x) +$ + +*2)* +$ + f(x)&=e^(3x)\ + f'(x)&=e^(3x) dot 3\ + &=3e^(3x) +$ + +*3)* +$ + f(x)&=e^(-x)\ + f'(x)&=e^(-x) dot (-1)\ + &=-e^(-x) +$ + +*4)* +$ + f(x)&=e^(0.5x)\ + f'(x)&=e^(0.5x) dot 1 / 2\ + &=1 / 2 e^(0.5x) +$ diff --git a/schule/mathe/pdfs/MA_2024-11-18.pdf b/schule/mathe/pdfs/MA_2024-11-18.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f22ba6c0dbac47f48c43cd8a9c0f3bebd2a18ba4 GIT binary patch literal 29531 zcmd431yo$yx~3fx+%*I*0s(?Mg}b{45AF^@f=dVxTml3L5+Jxc!QEYhySrPjO7=Nt z@7w#_`}ggCba$<9j8Id*DQi{MGv7I1DTs*CG0}4%zVZP+h=}YUMv$$61tJd*A_&Bw z;$~+IVi2>nae{nPb~bSO6#xllgoFs`I~qe`K@3vTDpHzaG&1G}#tu&AHqMU9#t!Bt zbV|mi&Q|&kbdpBKHcsYFZgdimY@#-XwnpYQrXYsDhKm?G8XDUe>DxF#3Uvf&aRA;Z z>HPAa68)Dh3rmVX%KTsU98x!sSJ}5u% zt7m{vplRlgP7ZD$DnY;xM$OvKrE-(uxh#9z8**HKfkc){O#0p$& zEMO2DaIvy-fY^bHnT-*|0l65Nfil4$R(3X^+c-h&EF2&vpeUe3R%Q?rP$UzGg#-BO zm;I`R1;oSxVrFLrG5s<&pe80Zh%s{j$=M;s21yPC19gFcC@{p>7=h%R5M$*8@-sq= zl^G0TW&$w-{sQ$g1HphnqF4b3e}@6C0{(JBN{1L53y>Vh1O{3LqyriYF`%uC5MyRx z2f}|DP!bC>#MmHdfiEn82W<45zz0ap3NcnNo6etS31r&*YnI3u+n73;0nV~PhT-=# z7naqxgM3q$g-o+w^IOc^%E{OP7$+-zCu0#~$ozwp2@JcjzBQt2vUQBK?Fu7$*P#dE zAyhE&G#E`tOH~40pf?>Y&f=1A#WzeOxmyy|u_G)E8-?M*9XIhoTdfT(@KkQ z)(CIuV>um`gy@YK#}T>gF>7U1w(W;Ni75OZ^OZhONPWNl@3ATX>qe!!QZ<7j%_UtPU_w5q?$=0YNnr~Iyo+<&4Ez! z0e-=1#GlSRuYy@yl2B(}@&$rw9B<4cz2#h%G@o{T>W=nTd<-%v6gqLldOw%j>fHg= z{)Q6n^eyP2d_^N_&*$Zed$^nWW^+iKQ9|xC=Ih?irtYK_W8iC+zr@vJFXwEp&SKi4 z-+9`M!;_N7PmWfKN@fq6Ch;CBcW>!U#02)8d_IXtV}THpMcmPZtWO4JBm)2}KGZY^E6OfVJN z_{e_YdBDSSZ8RJug%|!cLD1NS@_W%4WWfu{TgWWvPEr(Gu?pTR@edBR&V>6#gt zv8t=uN{w)n!S5ppVb?AD{NUOO=;2`VaFbleCCsKn;*eEsb5;r&h*$Lm->-AeD|?8H=-ruEzVhsGcr zR(&D#&<;eMI6|7{71897%Qe<~(QHVT#_E10kmWwsXZy^$R{AJfNSvx9<` zhTO&H!hPckdwSKJ@~|*4C^GtLlkMV(=TmzArqGQyi%W^VdW&#Fhz8|vv|F^KSH}!R zF^)4T_SW|Nrbatp5_^IrXU01D0|)fbFSMucN;Y$>r7&d)&@5-``p+&!>}ST}H;gE= zOicz*5Z$Rh;;`x%u=P7+Zm*}z>CrJ=I<34z+#TNW z-lzJ?5^%5P7d8`ZZVa9Jx@1dRh8xVPwvPhBf5!eug$b1WWJgBJlI5b z6tKWeCm~eqTqI%OT!!jpBewK4L+gH^7=-^!j1J4!(yW(;o*?$sUJRM%1q>?ua$j>d z)Ku-$Vf{Yq-mFWX*OAY_Nez+Ij8PUjuiiqH-CPhhzO zyZf2qhvDb^tWnAt?PJ*gh8skUhEE-_d+32gq8`-x4TD!aTjljcf~GNJKKvTp3t@sK z+WnOBRB$?LUZ37NS^lcnM&FbaGY3^_&FyoJ387kTuTkEMczFMenIk9?d*|VDuqORS zg4~tZ-A~41{ogqf&!I699JXLLf|p3j2B-Pl{V2cfk80sIXADKj4UbXEu+6qVdn2w@ z*(M3fwWuF`$#$~79$1D+8+LY%zGP0EP-=8o*0CH#P_`G%E6X;Bh-I#{Yp*1ZZ*6wU zrxjFPjqcE^Duolw(7O&waV%47_<^Z&C)nAeRy{Kp$ejn)EYXA)c6)Vl!pxcaB`P^3 z+P)##|Hx>>4AjMH7b*_W1fnNm3l@zgk3H7fMV zvEQ#Svt(51M-o8#qw<7L=H@5VvMcpa`~&pYSdK7{5K^Ak&-hilAWvR129=Y~ z$-OzPSV^Jsh_8N=?IG?@FETUv9ro1DiB%uBOXYG#^mVAe zZ19gn!RywD)anK=S~mq5yq#PoCFq(R@>bW&YYITj?zs_6Mw2-ynQemBDlXY>(!mYE z91WQ?3}zZ^QF%E;w$1s;Pm`_7hIzK}=QSI7YEZJ>)m~?>M8wCBrxzwEor5G+yi1fS zYPEtw$ICV)y71siN;>+2OzumV>~N)QBLzFn(c>}RY; 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