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cgawron/aufgabe.md

Created May 19, 2023 10:48
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Thomas' Matheproblem
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aufgabe.md

Wir zeigen:

$$\frac{\partial}{\partial t} \int_0^{\phi(t)} f(x) dx = \frac{\partial \phi}{\partial t}(t) f(\phi(t))$$

Physikerargumentation

Nach Kettenregel gilt

$$\frac{\partial}{\partial t} = \frac{\partial \phi}{\partial t} \frac{\partial}{\partial \phi}$$

Der Rest folgt aus dem Hauptsatz der Differential- und Integralrechnung:

$$\frac{\partial}{\partial t} \int_0^{t} f(x) dx = f(t)$$
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