d/(dt)(2e^tcos(t))

Lösung

\frac{d}{d t} (2 e^{t} cos (t))

2 (e^{t} cos (t) - e^{t} sin (t))

Schritte zur Lösung

\frac{d}{d t} (2 e^{t} cos (t))

Entferne die Konstante:

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

= 2 \frac{d}{d t} (e^{t} cos (t))

Wende die Produktregel an:

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

f = e^{t}, g = cos (t)

= 2 (\frac{d}{d t} (e^{t}) cos (t) + \frac{d}{d t} (cos (t)) e^{t})

\frac{d}{d t} (e^{t}) = e^{t}

\frac{d}{d t} (cos (t)) = - sin (t)

= 2 (e^{t} cos (t) + (- sin (t)) e^{t})

Vereinfache

= 2 (e^{t} cos (t) - e^{t} sin (t))

\frac{d P}{d t} + 2 tP = P + 6 t - 3

\int \frac{2 x + 5}{16 - 6 x - x ^{2}} d x

\int x^{3} x^{2} + 31 d x

x \to 0 lim (I n (x))

\int_{- 2}^{3} (x - 6) - (x^{2} - 12) d x