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Beliebt Rechnen >

derivative of 1/16 e^{2x^2}

Lösung

\frac{d}{d x} (\frac{1}{16} e^{2 x^{2}})

Lösung

\frac{e ^{2 x^{2}} x}{4}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{16} e^{2 x^{2}})

Entferne die Konstante:

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

= \frac{1}{16} \frac{d}{d x} (e^{2 x^{2}})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{2}) = 4 x

= \frac{1}{16} e^{2 x^{2}} \cdot 4 x

Vereinfache

\frac{1}{16} e^{2 x^{2}} \cdot 4 x : \frac{e ^{2 x^{2}} x}{4}

= \frac{e ^{2 x^{2}} x}{4}

Graph

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