derivative of (e^{-x^2}/(x^3))

Lösung

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

- \frac{e ^{- x^{2}} ( 2 x ^{2} + 3 )}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 e ^{- x^{2}} x ) x ^{3} - 3 x ^{2} e ^{- x^{2}}}{( x ^{3} ) ^{2}} : - \frac{e ^{- x^{2}} ( 2 x ^{2} + 3 )}{x ^{4}}

= - \frac{e ^{- x^{2}} ( 2 x ^{2} + 3 )}{x ^{4}}

d er i v a t i v e ln (6 - x^{2} + 2 x^{4})

\int_{1}^{\infty} \frac{7}{x ^{2} + 1} d x

d er i v a t i v e y = ((\frac{x ^{2} - 2}{2 x ^{2} + 1})^{2})

\int 6 d x

\frac{d}{d x} (∣ 2 x - 1 ∣)