(\partial)/(\partial x)(1/a e^{-(x/a)^2})

Lösung

\frac{\partial}{\partial x} (\frac{1}{a} e^{- (\frac{x}{a})^{2}})

- \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{a} e^{- (\frac{x}{a})^{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{a} \frac{\partial}{\partial x} (e^{- (\frac{x}{a})^{2}})

Wende die Kettenregel an:

e^{- (\frac{x}{a})^{2}} \frac{\partial}{\partial x} (- (\frac{x}{a})^{2})

= e^{- (\frac{x}{a})^{2}} \frac{\partial}{\partial x} (- (\frac{x}{a})^{2})

\frac{\partial}{\partial x} (- (\frac{x}{a})^{2}) = - \frac{2 x}{a ^{2}}

= \frac{1}{a} e^{- (\frac{x}{a})^{2}} (- \frac{2 x}{a ^{2}})

Vereinfache

\frac{1}{a} e^{- (\frac{x}{a})^{2}} (- \frac{2 x}{a ^{2}}) : - \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

= - \frac{2 e ^{- \frac{x ^{2}}{a ^{2}}} x}{a ^{3}}

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