arctan differenzieren

arctan

## Arkustangenz ableiten

$ f(x) = tan(x) $ und $ \bar f = arctan(x)$

$$ f(\bar f(x)) = x$$

$$ \frac{\delta f(\bar f(x))}{\delta x} = \frac{\delta x}{\delta x} $$

$$ \frac{\delta tan(arctan(x))}{\delta x} = \frac{\delta x}{\delta x} $$

> **Ableitung Tangenz** 
> $$\frac{\delta tan(x)}{dx} = 1 + tan(x)^2$$

> **Kettenregel**
> $$ \frac {\delta u(v(x))}{\delta x} = u'(v(x)) + v'(x) $$

$$ (1+tan(arctan(x))^2) * \frac{\delta arctan(x)}{\delta x} = 1 $$

$$ (1+x^2) * \frac{\delta arctan(x)}{\delta x} = 1 $$

$$ \frac{\delta arctan(x)}{\delta x} = \frac1{1+x^2} $$


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