((e^{-x^2})/(x^3))^'

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

(e^{- x^{2}})^{'} = - 2 e^{- x^{2}} 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}}

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