d/(dt)((x(t,C))(Ce^t))

Lösung

\frac{d}{d t} ((x (t, C)) (C e^{t}))

x C ((, C \cdot 1) e^{t} + e^{t} (t, C))

Schritte zur Lösung

\frac{d}{d t} ((x (t, C)) (C e^{t}))

Behandle

x, C

als Konstanten

Entferne die Konstante:

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

= x C \frac{d}{d t} ((t, C) e^{t})

Wende die Produktregel an:

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

f = t, C, g = e^{t}

= x C (\frac{d}{d t} (t, C) e^{t} + \frac{d}{d t} (e^{t}) (t, C))

\frac{d}{d t} (t, C) = (, C \cdot 1)

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

= x C ((, C \cdot 1) e^{t} + e^{t} (t, C))

f a c t or d^{3} e^{6} f^{9} - 216

f a c t or + a^{2} - x y + a x - a y

f a c t or 4 e^{2} + 7 e^{3} + 9 e^{4}

f a c t or \frac{x ^{2} - 3 x}{x}

f a c t or 3^{(n + 3)} - 27