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Beliebt Rechnen >

derivative (t^2+1)(t-1/t)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = t^{2} + 1, g = t - \frac{1}{t}

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

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

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

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

Vereinfache

2 t (t - \frac{1}{t}) + (1 + \frac{1}{t ^{2}}) (t^{2} + 1) : 3 t^{2} + \frac{1}{t ^{2}}

= 3 t^{2} + \frac{1}{t ^{2}}

Graph

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