derivative y=(t^2+8)^2-2(t^2+8)

Lösung

ableitung von

y = (t^{2} + 8)^{2} - 2 (t^{2} + 8)

4 t^{3} + 28 t

Schritte zur Lösung

\frac{d}{d t} ((t^{2} + 8)^{2} - 2 (t^{2} + 8))

Vereinfache

(t^{2} + 8)^{2} - 2 (t^{2} + 8) : t^{4} + 14 t^{2} + 48

= \frac{d}{d t} (t^{4} + 14 t^{2} + 48)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (t^{4}) + \frac{d}{d t} (14 t^{2}) + \frac{d}{d t} (48)

\frac{d}{d t} (t^{4}) = 4 t^{3}

\frac{d}{d t} (14 t^{2}) = 28 t

\frac{d}{d t} (48) = 0

= 4 t^{3} + 28 t + 0

Vereinfache

= 4 t^{3} + 28 t

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