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Beliebt Rechnen >

d/(dt)(e^t*cos(t))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

steigung (1/2 ,2),(6,2)

s l o p e (\frac{1}{2}, 2), (6, 2)

integral from-3 to 0 of 1/(9+2x)

\int_{- 3}^{0} \frac{1}{9 + 2 x} d x

integral of xe^x-x

\int x e^{x} - x d x

integral of arcsin(x+2)

\int arcsin (x + 2) d x

inverselaplace 1/(s^3-2s^2+3s)

in v erse l a pl a ce \frac{1}{s ^{3} - 2 s ^{2} + 3 s}