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Mathematik mit der HBS12

Ableitung - Level 1

1
Bestimme die Ableitungen von folgenden Funktionen. Die Lösungen findest Du zum Überprüfen auf der zweiten Seite.
  • f(x)=x2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=x^2

  • f(x)=5x4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=5x^4

  • f(x)=3x2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=-3x^2

  • f(x)=2x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=2x^{-3}

  • f(x)=0,1x10\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=-0{,}1x^{10}

  • f(x)=27x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=27x^3

  • f(x)=16x6\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=\frac{1}{6}x^6

  • f(x)=12x1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=12x^{-1}

  • f(x)=x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=x

  • f(x)=4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=4

  • f(x)=7x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=7x

  • f(x)=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f(x)=0

  • f(x)=20x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=20x^3
2
Hier die Lösungen:
  • f(x)=2x1=2x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=2x^1=2x

  • f(x)=54x3=20x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=5\cdot4x^3=20x^3

  • f(x)=32x1=6x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=-3\cdot2x^1=-6x

  • f(x)=2(3)x4=6x4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=2\cdot(-3)x^{-4}=-6x^{-4}

  • f(x)=0,110x9=x9\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=-0{,}1\cdot10x^9=-x^9

  • f(x)=273x2=81x2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=27\cdot3x^2=81x^2

  • f(x)=166x5=x5\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=\frac{1}{6}\cdot6x^5=x^5

  • f(x)=12(1)x2=12x2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=12*(-1)x^{-2}=-12x^{-2}

  • f(x)=1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=1

  • f(x)=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=0

  • f(x)=7\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=7

  • f(x)=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f'(x)=0

  • f(x)=203x2=60x2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} f''(x)=20\cdot3x^2=60x^2