Benutzer:MovGP0/Mathematik/Ableitung

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Physik Mathematische Grundlagen Mathematik für ET Semester 1 • Semester 2 • Semester 3 Mathematik Kombinatorik und Permutationen • Ableitung • Dreiecksnotation • Gradient, Divergenz, Rotation • Metrischer Tensor • Christoffelsymbole • Krümmungstensor • Energie-Impuls-Tensor • Kosmologische Konstante Quantenmechanik mit Matrizen Imaginäre und komplexe Zahlen • Vektoren • Matrizen • Jacobi-Matrizen • Pauli-Matrizen • Hermitesche Matrizen Lineare Algebra und Tensoren Tensornotation • Tensoren • Dirac-Notation • Körper • Vektorraum Gruppentheorie Gruppen, Lie Gruppen, Lie Algebren Ableitungen Ableitungsregeln Konstante ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}{\color {brown}n}={\color {brown}0}$ Faktorregel ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}\left({\color {brown}n}\cdot {\color {PineGreen}f({\color {blue}x})}\right)={\color {brown}n}\cdot {\color {PineGreen}f'({\color {blue}x})}$ Potenzregel ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}{\color {blue}x}^{\color {brown}n}={\color {brown}n}{\color {blue}x}^{\color {brown}n-1}$ Produktregel ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}\left({\color {PineGreen}f({\color {blue}x})}{\color {brown}g({\color {blue}x})}\right)={\color {PineGreen}f'({\color {blue}x})}\cdot {\color {brown}g({\color {blue}x})}+{\color {PineGreen}f({\color {blue}x})}\cdot {\color {brown}g'({\color {blue}x})}$ Kettenregel ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}\left({\color {PineGreen}f({\color {brown}g({\color {blue}x})})}\right)=({\color {PineGreen}f}\circ {\color {brown}g})'({\color {blue}x})={\color {PineGreen}f'({\color {brown}g({\color {blue}x})})}\cdot {\color {brown}g'({\color {blue}x})}$ Quotientenregel ${\frac {\mathrm {d} }{\mathrm {d} {\color {blue}x}}}\left({\frac {\color {PineGreen}f({\color {blue}x})}{\color {brown}g({\color {blue}x})}}\right)={\frac {{\color {PineGreen}f'({\color {blue}x})}\cdot {\color {brown}g({\color {blue}x})}-{\color {PineGreen}f({\color {blue}x})}\cdot {\color {brown}g'({\color {blue}x})}}{{\color {brown}g({\color {blue}x})}^{2}}}={\frac {\color {PineGreen}f'({\color {blue}x})}{\color {brown}g({\color {blue}x})}}-{\frac {{\color {PineGreen}f({\color {blue}x})}\cdot {\color {brown}g'({\color {blue}x})}}{{\color {brown}g({\color {blue}x})}^{2}}}$ Siehe auch Tabelle von Ableitungs- und Stammfunktionen