d/(dt)({v}(t)t)

Lösung

\frac{d}{d t} (v (t) t)

t \frac{d}{d t} (v (t)) + v (t)

Schritte zur Lösung

\frac{d}{d t} (v (t) t)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = v (t), g = t

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

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

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

Vereinfache

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

\frac{\partial}{\partial x} (x^{2} - 2 x y)

\int \frac{4 + x ^{2}}{x} d x

x \to - 3 lim (x^{2} - 9)

x \to 7 - lim (\frac{2}{x + 7})

\frac{d}{d x} (e^{(\frac{1}{x})})