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^tcos(2t))

Lösung

\frac{d}{d t} (e^{t} cos (2 t))

Lösung

e^{t} cos (2 t) - 2 e^{t} sin (2 t)

Schritte zur Lösung

\frac{d}{d t} (e^{t} cos (2 t))

Wende die Produktregel an:

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

f = e^{t}, g = cos (2 t)

= \frac{d}{d t} (e^{t}) cos (2 t) + \frac{d}{d t} (cos (2 t)) e^{t}

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

\frac{d}{d t} (cos (2 t)) = - sin (2 t) \cdot 2

= e^{t} cos (2 t) + (- sin (2 t) \cdot 2) e^{t}

Vereinfache

= e^{t} cos (2 t) - 2 e^{t} sin (2 t)

Graph

Beliebte Beispiele

derivative x^2ln(x^2)

d er i v a t i v e x^{2} ln (x^{2})

limit as x approaches 0 of \sqrt[2x]{a}

x \to 0 lim (2 x a)

derivative y=(5x+4)^3

d er i v a t i v e y = (5 x + 4)^{3}

1 - y^{^{'}} = cos (y)

integral from 2 to 3 of 3/(sqrt(3-x))

\int_{2}^{3} \frac{3}{3 - x} d x