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Beliebt Rechnen >

derivative of (e^x/(1-x))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{1 - x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{1 - x})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (1 - x) = - 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative f(x)=(x-2/x)

d er i v a t i v e f (x) = (x - \frac{2}{x})

derivative of ((e^x)/(1+x^2))

\frac{d}{d x} (\frac{( e ^{x} )}{1 + x ^{2}})

sum from n=1 to infinity of ln(n)

n = 1 \sum \infty ln (n)

limit as x approaches b of 7(-7)

x \to b lim (7 (- 7))

(dx)/(dt)= 1/(xe^{t+2x)}

\frac{d x}{d t} = \frac{1}{x e ^{t + 2 x}}