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

Lösung

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

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

Schritte zur Lösung

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

Behandle

c, t

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

\frac{( x + 1 ) d y}{d x} + (x + 2) y = 2 x e^{- x}

\int \frac{c}{x} d x

x \to 0.1 lim (\frac{e ^{5 x} - 1}{x})

4 y^{^{''}} + 36 y^{^{'}} + 81 y = 0

t an g e n t - 3 x^{2} + 6 x - 2