d/(dt)((h(t))(4t+10))

Lösung

\frac{d}{d t} ((h (t)) (4 t + 10))

h (8 t + 10)

Schritte zur Lösung

\frac{d}{d t} ((h (t)) (4 t + 10))

Behandle

h

als Konstante

Entferne die Konstante:

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

= h \frac{d}{d t} (t (4 t + 10))

Wende die Produktregel an:

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

f = t, g = 4 t + 10

= h (\frac{d t}{d t} (4 t + 10) + \frac{d}{d t} (4 t + 10) t)

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

\frac{d}{d t} (4 t + 10) = 4

= h (1 \cdot (4 t + 10) + 4 t)

Vereinfache

= h (8 t + 10)

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