d/(dt)(((i+2t))/((t-i)))

Lösung

\frac{d}{d t} (\frac{( i + 2 t )}{( t - i )})

- \frac{3 i}{( t - i ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{( i + 2 t )}{( t - i )})

Wende die Quotientenregel an:

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

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

\frac{d}{d t} (i + 2 t) = 2

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

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

Vereinfache

\frac{2 ( t - i ) - 1 \cdot ( i + 2 t )}{( t - i ) ^{2}} : - \frac{3 i}{( t - i ) ^{2}}

= - \frac{3 i}{( t - i ) ^{2}}

f a c t or x^{3} + 5 x^{2} + 6 x

lo g_{2} (\frac{t - 8}{2 t}) < lo g_{2} (3) - 7

f a c t or x^{3} - 17 x - 4

x^{2} = 6 x - 15

- 4 x - 7 - 3 x + 4 = 25