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

Lösung

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

12 c e^{s i n (x + 4 c t)} cos (x + 4 c t)

Schritte zur Lösung

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

Behandle

c, x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial t} (sin (x + 4 c t)) = cos (x + 4 c t) \cdot 4 c

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

Vereinfache

= 12 c e^{s i n (x + 4 c t)} cos (x + 4 c t)

f (x) = x^{6 x}

y^{^{'}} = \frac{( 4 x ^{3} + y ^{3} )}{x y ^{2}}

n = 0 \sum \infty \frac{1}{2 n !}

y^{^{'}} = cos^{2} (y) ln (x)

\frac{\partial}{\partial x} (e^{5 x} sin (5 y))