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Beliebt Rechnen >

derivative f(t)=0.1(400-40t+t^2)

Lösung

ableitung von

f (t) = 0.1 (400 - 40 t + t^{2})

Lösung

0.1 (2 t - 40)

Schritte zur Lösung

\frac{d}{d t} (0.1 (400 - 40 t + t^{2}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.1 \frac{d}{d t} (400 - 40 t + t^{2})

Wende die Summen-/Differenzregel an:

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

= 0.1 (\frac{d}{d t} (400) - \frac{d}{d t} (40 t) + \frac{d}{d t} (t^{2}))

\frac{d}{d t} (400) = 0

\frac{d}{d t} (40 t) = 40

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

= 0.1 (0 - 40 + 2 t)

Vereinfache

= 0.1 (2 t - 40)

Graph

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