derivative of (e^{x^2}/(2x))

Lösung

\frac{d}{d x} (\frac{e ^{x^{2}}}{2 x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x^{2}}}{2 x})

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

\frac{d x}{d x} = 1

= \frac{1}{2} \cdot \frac{e ^{x^{2}} \cdot 2 xx - 1 \cdot e ^{x^{2}}}{x ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{e ^{x^{2}} \cdot 2 xx - 1 \cdot e ^{x^{2}}}{x ^{2}} : \frac{2 e ^{x^{2}} x ^{2} - e ^{x^{2}}}{2 x ^{2}}

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

\frac{d}{d x} (e^{- x^{2} - y^{2}})

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