d/(dt)(({z}(t))(-10sin(t)+2cos(t)))

Lösung

\frac{d}{d t} ((z (t)) (- 10 sin (t) + 2 cos (t)))

\frac{d}{d t} (z (t)) (- 10 sin (t) + 2 cos (t)) + (- 10 cos (t) - 2 sin (t)) z (t)

Schritte zur Lösung

\frac{d}{d t} ((z (t)) (- 10 sin (t) + 2 cos (t)))

Wende die Produktregel an:

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

f = z (t), g = - 10 sin (t) + 2 cos (t)

= \frac{d}{d t} (z (t)) (- 10 sin (t) + 2 cos (t)) + \frac{d}{d t} (- 10 sin (t) + 2 cos (t)) z (t)

\frac{d}{d t} (- 10 sin (t) + 2 cos (t)) = - 10 cos (t) - 2 sin (t)

= \frac{d}{d t} (z (t)) (- 10 sin (t) + 2 cos (t)) + (- 10 cos (t) - 2 sin (t)) z (t)

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

e x p an d (s + 2 π)^{2}

\frac{d}{d r} ((r) (\frac{8 π r}{3} - \frac{2 v}{r}))

\frac{d ^{2}}{d h ^{2}} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

e x p an d \frac{( r + i x ) - 1}{( r + i x ) + 1}