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Beliebt Rechnen >

d/(dt)(t-1/t)

Lösung

\frac{d}{d t} (t - \frac{1}{t})

Lösung

1 + \frac{1}{t ^{2}}

Schritte zur Lösung

\frac{d}{d t} (t - \frac{1}{t})

Wende die Summen-/Differenzregel an:

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

= \frac{d t}{d t} - \frac{d}{d t} (\frac{1}{t})

\frac{d t}{d t} = 1

\frac{d}{d t} (\frac{1}{t}) = - \frac{1}{t ^{2}}

= 1 - (- \frac{1}{t ^{2}})

Vereinfache

= 1 + \frac{1}{t ^{2}}

Graph

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