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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (cos^{5} (3 x))

\frac{\partial}{\partial x} (9)

y^{^{'}} = a^{x + y}

\int \frac{x}{x - x ^{2}} d x

\frac{d}{d x} (6 ln (4 x))