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 0000000..f22ba6c Binary files /dev/null and b/schule/mathe/pdfs/MA_2024-11-18.pdf differ