# Abitur Formelsammlung


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# Andere Formelsammlung
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# Nochmal andere Formelsammlung
https://www.plus.ac.at/wp-content/uploads/2021/02/Formelsammlung_-_Mathematik_1_und_2.pdf

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# Nochmal was anderes
https://mmf.univie.ac.at/fileadmin/user_upload/p_mathematikmachtfreunde/Materialien/Formelsammlung-Angewandte_Mathematik.pdf

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# Chatgpt 
![[Pasted image 20250129153437.png]]https://chatgpt.com/share/679a3c80-ac54-8006-a47c-8e96230a1210

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# Vorherige Formelsammlungen
### Ableitungen
>Nicht Aufgelistet sind Ableitung die trivial sind.

| **$f(x)$**          | **$f'(x)$**                                          | **$F(x)$**                                                       |
| ------------------- | ---------------------------------------------------- | ---------------------------------------------------------------- |
| $x^n$               | $n \cdot x^{n-1}$                                    | $\frac{x^{n+1}}{n+1} + C$                                        |
| $c \cdot f(x)$      | $c \cdot f'(x)$                                      | $c \cdot \int f(x)\,dx + C$                                      |
| $f(x) \cdot g(x)$   | $f'(x) \cdot g(x) + f(x) \cdot g'(x)$                | $\int f(x)g(x)\,dx + C$                                          |
| $\frac{f(x)}{g(x)}$ | $\frac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{g(x)^2}$ | $\int \frac{f(x)}{g(x)}\,dx + C$                                 |
| $f(g(x))$           | $f'(g(x)) \cdot g'(x)$                               | $\int f(g(x))\,dx + C$                                           |
| $\ln(x)$            | $\frac{1}{x}$                                        | $x \ln(x) - x + C$                                               |
| $\ln(a \cdot x)$    | $\frac{1}{x}$                                        | $x \ln(a x) - x + C$                                             |
| $\ln(g(x))$         | $\frac{g'(x)}{g(x)}$                                 | $x \ln(g(x)) - \int \frac{x g'(x)}{g(x)}\,dx + C$                |
| $\log_a(x)$         | $\frac{1}{x \cdot \ln(a)}$                           | $\frac{x \ln(x) - x}{\ln(a)} + C$                                |
| $\log_b(g(x))$      | $\frac{g'(x)}{g(x) \cdot \ln(b)}$                    | $\frac{x \ln(g(x)) - \int \frac{x g'(x)}{g(x)}\,dx}{\ln(b)} + C$ |
| $a^x$               | $a^x \cdot \ln(a)$                                   | $\frac{a^{x}}{\ln(a)} + C$                                       |
| $\sqrt{x}$          | $\frac{1}{2\sqrt{x}}$                                | $\frac{2}{3} x^{3/2} + C$                                        |
| $\sin(x)$           | $\cos(x)$                                            | $-\cos(x) + C$                                                   |
| $\cos(x)$           | $-\sin(x)$                                           | $\sin(x) + C$                                                    |
| $\tan(x)$           | $\frac{1}{\cos^2(x)}$                                | $-\ln ( \| \cos(x) \|) + C$                                      |


# O1 Formelsammlung