d/(dt)((x)(xsin(wt+c)))

Lösung

\frac{d}{d t} ((x) (x sin (wt + c)))

x^{2} cos (wt + c) w

Schritte zur Lösung

\frac{d}{d t} ((x) (x sin (wt + c)))

Vereinfache

(x) (x sin (wt + c)) : x^{2} sin (wt + c)

= \frac{d}{d t} (x^{2} sin (wt + c))

Behandle

c, x, w

als Konstanten

Entferne die Konstante:

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

= x^{2} \frac{d}{d t} (sin (wt + c))

Wende die Kettenregel an:

cos (wt + c) \frac{d}{d t} (wt + c)

= cos (wt + c) \frac{d}{d t} (wt + c)

\frac{d}{d t} (wt + c) = w

= x^{2} cos (wt + c) w

f a c t or 4 x^{2} - 12 x^{2}

f a c t or 3 x^{3} + 3 x^{2} - 2 x^{0.3}

f a c t or (4 x^{2} + 2 y) + (3 x + y^{2})

f a c t or 9 (x - 2)^{2} - 24 (x - 2) + 16

f a c t or 10 cos^{2} (x) + cos (x) - 11