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Beliebt Algebra >

d/(dt)((x)(cos(t)))

Lösung

\frac{d}{d t} ((x) (cos (t)))

Lösung

cos (t) \frac{d x}{d t} - sin (t) x

Schritte zur Lösung

\frac{d}{d t} ((x) (cos (t)))

Wende die Produktregel an:

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

f = x, g = cos (t)

= \frac{d x}{d t} cos (t) + \frac{d}{d t} (cos (t)) x

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

= \frac{d x}{d t} cos (t) + (- sin (t)) x

Vereinfache

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

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