d/(dt)((r)(rcos(t)))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

(r) (r cos (t)) : cos (t) r^{2}

= \frac{d}{d t} (cos (t) r^{2})

Wende die Produktregel an:

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

f = cos (t), g = r^{2}

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

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

\frac{d}{d t} (r^{2}) = 2 r \frac{d r}{d t}

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

Vereinfache

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

f a c t or \frac{5}{7} - \frac{2}{3}

f a c t or 125 x^{3} - 27 x^{3}

f a c t or x^{3} - 3 x^{2} 4 x + 12

f a c t or y^{2} - y^{2}

s im pl i f y x^{(n - 1)}