d/(dt)(t/(t-1))

Lösung

\frac{d}{d t} (\frac{t}{t - 1})

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

Schritte zur Lösung

\frac{d}{d t} (\frac{t}{t - 1})

Wende die Quotientenregel an:

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

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

\frac{d t}{d t} = 1

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

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

Vereinfache

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

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

d er i v a t i v e 4 t e^{- t}

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

a re a x^{2} - 3 x, 5 x, [0, 8]

\frac{d y}{d x} + y = 2 x y^{2} e x

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})