(\partial)/(\partial x)(ln(1-e^{-x}))

Lösung

\frac{\partial}{\partial x} (ln (1 - e^{- x}))

\frac{e ^{- x}}{1 - e ^{- x}}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (1 - e^{- x}))

Wende die Kettenregel an:

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

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

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

= \frac{1}{1 - e ^{- x}} e^{- x}

Vereinfache

\frac{1}{1 - e ^{- x}} e^{- x} : \frac{e ^{- x}}{1 - e ^{- x}}

= \frac{e ^{- x}}{1 - e ^{- x}}

\frac{d}{d x} (arctan (\frac{x}{a}))

\frac{\partial}{\partial y} (e^{2 x} \cdot sin (y))

d er i v a t i v e y = \frac{x ^{3}}{( x - 1 ) ^{2}}

\int cos (x) (2 + 7 sin^{2} (x)) d x

x \to \infty lim (\frac{2 ^{x + 1} + 3 ^{x}}{2 ^{x} + 3 ^{x + 1}})