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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int 8 t^{3} (1 + t^{4})^{10} d t

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d er i v a t i v e f (x) = x \cdot e^{x}