d/(dt)((3t^2-3)/(2t))

Lösung

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

\frac{3 t ^{2} + 3}{2 t ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d t} (\frac{3 t ^{2} - 3}{t})

Wende die Quotientenregel an:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d t} ( 3 t ^{2} - 3 ) t - \frac{d t}{d t} ( 3 t ^{2} - 3 )}{t ^{2}}

\frac{d}{d t} (3 t^{2} - 3) = 6 t

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

= \frac{1}{2} \cdot \frac{6 tt - 1 \cdot ( 3 t ^{2} - 3 )}{t ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{6 tt - 1 \cdot ( 3 t ^{2} - 3 )}{t ^{2}} : \frac{3 t ^{2} + 3}{2 t ^{2}}

= \frac{3 t ^{2} + 3}{2 t ^{2}}

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

\int_{0}^{1} \frac{27}{4 y - 1} d y

n = 1 \sum \infty 1 0^{n} x^{n} n!

d er i v a t i v e 2 x + 5

s l o p e in t erce pt (4) (8.6)