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Beliebt Rechnen >

d/(dt)(cos(t)+tsin(t))

Lösung

\frac{d}{d t} (cos (t) + t sin (t))

Lösung

t cos (t)

Schritte zur Lösung

\frac{d}{d t} (cos (t) + t sin (t))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - sin (t) + sin (t) + t cos (t)

Vereinfache

= t cos (t)

Graph

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d er i v a t i v e f (x) = \frac{4 x}{( x ^{2} + 1 )}