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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

\int_{- 1}^{1} e^{y} - (y^{2} - 9) d y

(14 - 6 y + e - 3 x) d x - 2 d y = 0

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x

\int sin^{4} (x co) s^{2} x d x

d er i v a t i v e y = \frac{cos ( x )}{x ^{7}}