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Beliebt Rechnen >

d/(dt)(e^{-2t}{y}(t))

Lösung

\frac{d}{d t} (e^{- 2 t} y (t))

Lösung

- 2 e^{- 2 t} y (t) + e^{- 2 t} \frac{d}{d t} (y (t))

Schritte zur Lösung

\frac{d}{d t} (e^{- 2 t} y (t))

Wende die Produktregel an:

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

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

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

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

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

Vereinfache

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

Beliebte Beispiele

derivative 2sin(2x)

d er i v a t i v e 2 sin (2 x)

derivative f(x)=sqrt(3x+7)

d er i v a t i v e f (x) = 3 x + 7

integral of 2x^2+4

\int 2 x^{2} + 4 d x

limit as x approaches 7+of x

x \to 7 + lim (x)

integral from-2 to 3 of (13)/(x^4)

\int_{- 2}^{3} \frac{13}{x ^{4}} d x