d/(dt)((e^{-t})/(1+t^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d t} (1 + t^{2}) = 2 t

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

Vereinfache

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

d er i v a t i v e arcsec (x) \cdot arccos (x)

\int t e^{t + 2} d t

\int \frac{d m}{m ^{3} + m ^{2}} d x

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{7 r ^{\frac{6}{7}}})

\int cos (t) sin^{4} (t) d t