d/(dt)((θ(t))(4.1t+12.6t^2))

Lösung

\frac{d}{d t} ((θ (t)) (4.1 t + 12.6 t^{2}))

θ (37.8 t^{2} + 8.2 t)

Schritte zur Lösung

\frac{d}{d t} ((θ (t)) (4.1 t + 12.6 t^{2}))

Behandle

θ

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= θ \frac{d}{d t} (t (4.1 t + 12.6 t^{2}))

Wende die Produktregel an:

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

f = t, g = 4.1 t + 12.6 t^{2}

= θ (\frac{d t}{d t} (4.1 t + 12.6 t^{2}) + \frac{d}{d t} (4.1 t + 12.6 t^{2}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (4.1 t + 12.6 t^{2}) = 4.1 + 25.2 t

= θ (1 \cdot (4.1 t + 12.6 t^{2}) + (4.1 + 25.2 t) t)

Vereinfache

θ (1 \cdot (4.1 t + 12.6 t^{2}) + (4.1 + 25.2 t) t) : θ (37.8 t^{2} + 8.2 t)

= θ (37.8 t^{2} + 8.2 t)

e x p an d (X + X Y^{^{'}}) [Y + XZ (Y + XZ) + Y^{^{'}}]

e x p an d \frac{x ^{2} - 2 x - 1}{( x ^{2} + 1 ) ^{2}}

e x p an d \frac{1}{( s + 2 ) ( s ^{2} + 3 )}

e x p an d (x - 1) e

e x p an d \frac{1}{( x ^{5} + 4 x ) ^{3} - 6}