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Beliebt Rechnen >

d/(dt)(e^tsin(t))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

derivative 400x^{10}+40x^5+1

d er i v a t i v e 400 x^{10} + 40 x^{5} + 1

derivative of 2/(1-x^3)

\frac{d}{d x} (\frac{2}{1 - x ^{3}})

integral of cot(6x)

\int cot (6 x) d x

derivative x^2sin^2(5x)

d er i v a t i v e x^{2} sin^{2} (5 x)

derivative y=5e^x

d er i v a t i v e y = 5 e^{x}