derivative of (e^x/(x^7))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{x ^{7}})

\frac{e ^{x} ( x - 7 )}{x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{x ^{7}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{x} ) x ^{7} - \frac{d}{d x} ( x ^{7} ) e ^{x}}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}}

Vereinfache

\frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}} : \frac{e ^{x} ( x - 7 )}{x ^{8}}

= \frac{e ^{x} ( x - 7 )}{x ^{8}}

\int a^{5 x} d x

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