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Beliebt Rechnen >

derivative f(t)=sin(t)-tcos(t)

Lösung

ableitung von

f (t) = sin (t) - t cos (t)

Lösung

t sin (t)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

= t sin (t)

Graph

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