derivative of x^{-2}e^x

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = e^{x}

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

= (- \frac{2}{x ^{3}}) e^{x} + e^{x} x^{- 2}

Vereinfache

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

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

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