d/(dt)(e^{-at}cos(wt))

Lösung

\frac{d}{d t} (e^{- a t} cos (wt))

- a e^{- a t} cos (tw) - e^{- a t} w sin (tw)

Schritte zur Lösung

\frac{d}{d t} (e^{- a t} cos (wt))

Behandle

a, w

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

= - a e^{- a t} cos (tw) - e^{- a t} w sin (tw)

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

\frac{d}{d x} (\frac{( 3 x ^{2} + 1 ) ^{3}}{( 2 x ^{2} - 1 ) ^{4}})

f^{^{'}} (x) = a^{2 x}

n = 1 \sum \infty (\frac{n - 2}{n})^{n}

\int (sin (2 u) - cos (3 u))^{(2)} d u