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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

a re a x, x^{\frac{1}{2}}, 1, 2

\int 2 5 x^{3} - 3 x d x

y^{^{'}} = y + x^{2}

\frac{d y}{d x} = \frac{x ( e ^{x^{2}} + 2 )}{6 y ^{2}}

d er i v a t i v e y = (6 x - 2) (5 x + 7)