derivative of e^{(-x^2/8})

Soluzione

\frac{d}{d x} (e^{\frac{- x ^{2}}{8}})

- \frac{e ^{- \frac{x ^{2}}{8}} x}{4}

Fasi della soluzione

\frac{d}{d x} (e^{\frac{- x ^{2}}{8}})

Semplifica

e^{\frac{- x ^{2}}{8}} : e^{- \frac{x ^{2}}{8}}

= \frac{d}{d x} (e^{- \frac{x ^{2}}{8}})

Applica la regola della catena:

e^{- \frac{x ^{2}}{8}} \frac{d}{d x} (- \frac{x ^{2}}{8})

= e^{- \frac{x ^{2}}{8}} \frac{d}{d x} (- \frac{x ^{2}}{8})

\frac{d}{d x} (- \frac{x ^{2}}{8}) = - \frac{x}{4}

= e^{- \frac{x ^{2}}{8}} (- \frac{x}{4})

Semplificare

e^{- \frac{x ^{2}}{8}} (- \frac{x}{4}) : - \frac{e ^{- \frac{x ^{2}}{8}} x}{4}

= - \frac{e ^{- \frac{x ^{2}}{8}} x}{4}

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