(\partial)/(\partial t)(4e^{sin(x+3ct)})

Lösung

\frac{\partial}{\partial t} (4 e^{s i n (x + 3 c t)})

12 c e^{s i n (x + 3 c t)} cos (x + 3 c t)

Schritte zur Lösung

\frac{\partial}{\partial t} (4 e^{s i n (x + 3 c t)})

Behandle

c, x

als Konstante

Entferne die Konstante:

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

= 4 \frac{\partial}{\partial t} (e^{s i n (x + 3 c t)})

Wende die Kettenregel an:

e^{s i n (x + 3 c t)} \frac{\partial}{\partial t} (sin (x + 3 c t))

= e^{s i n (x + 3 c t)} \frac{\partial}{\partial t} (sin (x + 3 c t))

\frac{\partial}{\partial t} (sin (x + 3 c t)) = cos (x + 3 c t) \cdot 3 c

= 4 e^{s i n (x + 3 c t)} cos (x + 3 c t) \cdot 3 c

Vereinfache

= 12 c e^{s i n (x + 3 c t)} cos (x + 3 c t)

x \to - 5 lim (\frac{2}{( x + 5 ) ^{4}})

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