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}}

\int \frac{x}{4} d x

x \to 8 lim (\frac{∣ x - 8 ∣}{x - 8})

x \to 6 + lim (\frac{2 + x}{6 - x})

d er i v a t i v e f (x) = 3 x^{2 x + 3} + e^{2}

x \to 0 lim (e^{x} sin (x))