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

Lösung

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

\frac{- 3 e ^{- x^{3}} x ^{3} - e ^{- x^{3}}}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

= \frac{( - 3 e ^{- x^{3}} x ^{2} ) x - 1 \cdot e ^{- x^{3}}}{x ^{2}}

Vereinfache

\frac{( - 3 e ^{- x^{3}} x ^{2} ) x - 1 \cdot e ^{- x^{3}}}{x ^{2}} : \frac{- 3 e ^{- x^{3}} x ^{3} - e ^{- x^{3}}}{x ^{2}}

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

in v erse l a pl a ce \frac{1}{s ^{2} + 2 s + 10}

\int \frac{5 x ^{2}}{( x - 2 ) ( x ^{2} + 4 )} d x

\frac{d}{d x} (x + 1 \cdot e^{x})

t an g e n t \frac{7}{x ^{2}}

\int tan^{5} (4 x) d x