de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

d/(dt)(e^{4t}cos(t))

Lösung

\frac{d}{d t} (e^{4 t} cos (t))

Lösung

4 e^{4 t} cos (t) - e^{4 t} sin (t)

Schritte zur Lösung

\frac{d}{d t} (e^{4 t} cos (t))

Wende die Produktregel an:

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

f = e^{4 t}, g = cos (t)

= \frac{d}{d t} (e^{4 t}) cos (t) + \frac{d}{d t} (cos (t)) e^{4 t}

\frac{d}{d t} (e^{4 t}) = e^{4 t} \cdot 4

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

= e^{4 t} \cdot 4 cos (t) + (- sin (t)) e^{4 t}

Vereinfache

= 4 e^{4 t} cos (t) - e^{4 t} sin (t)

Graph

Beliebte Beispiele

derivative of (7x-4/(-3x+3))

\frac{d}{d x} (\frac{7 x - 4}{- 3 x + 3})

d er i v a t i v e - 6

limit as x approaches 5 of 2x-5

x \to 5 lim (2 x - 5)

(dy)/(dt)=(1+t)(1+y)

\frac{d y}{d t} = (1 + t) (1 + y)

limit as t approaches 1+of (|1-t|)/(1-t)

t \to 1 + lim (\frac{∣ 1 - t ∣}{1 - t})