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

Lösung

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

\frac{d}{d t} (r (t)) (2 sin (t) - e^{- t}) + (2 cos (t) + e^{- t}) r (t)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

e x p an d (\frac{x}{3} + \frac{y}{6} + z = 1) 6

e x p an d \frac{9 + 27 s + 3 s ^{3}}{( 9 + s ^{2} ) ^{2}}

e x p an d \frac{( 0.37 + 2 x ) ^{2}}{( 0.3 - x ) \cdot ( 0.38 - x )}

e x p an d 2 π (2 + ln (1 + 2))

s im pl i f y \frac{31.622}{( s + 0.5 ) ( s + 1 ) ^{2}}