7.3 Ableitung der natürlichen Exponentialfunktion

f (x) = \ln x

```col-md
![Pasted image 20240426145722.png](/img/user/06%20Sources/Anh%C3%A4nge%20Abitur/Anh%C3%A4nge%20Mathematik/Zeichnungen/Pasted%20image%2020240426145722.png)
```
```col-md

| $x$   | Steigung      |
| ----- | ------------- |
| $0,5$ | $2$           |
| $1$   | $1$           |
| $2$   | $\frac{1}{2}$ |
| $3$   | $\frac{1}{3}$ |
| $4$   | $\frac{1}{4}$ |
| $5$   | $\frac{1}{5}$ |
| $6$   | $\frac{1}{6}$ |

```

\begin{aligned} f (x) = \ln (x) ⟹ f^{'} (x) = \frac{1}{x} \\ \ln (2 x) ⟹ f^{'} (x) = \frac{1}{2 x} \cdot 2 \\ f^{'} (x) = \frac{1}{x} \\ f (x) = \ln (4 - 2 x) ⟹ f^{'} (x) = - 2 \frac{1}{4 - 2 x} \\ f (x) = \ln (4 - x^{2}) ⟹ f^{'} (x) = - 2 x \frac{1}{4 - x^{2}} \end{aligned}