derivative (4t^2-t)(t^3-8t^2+12)

Lösung

ableitung von

(4 t^{2} - t) (t^{3} - 8 t^{2} + 12)

20 t^{4} - 132 t^{3} + 24 t^{2} + 96 t - 12

Schritte zur Lösung

\frac{d}{d t} ((4 t^{2} - t) (t^{3} - 8 t^{2} + 12))

Wende die Produktregel an:

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

f = 4 t^{2} - t, g = t^{3} - 8 t^{2} + 12

= \frac{d}{d t} (4 t^{2} - t) (t^{3} - 8 t^{2} + 12) + \frac{d}{d t} (t^{3} - 8 t^{2} + 12) (4 t^{2} - t)

\frac{d}{d t} (4 t^{2} - t) = 8 t - 1

\frac{d}{d t} (t^{3} - 8 t^{2} + 12) = 3 t^{2} - 16 t

= (8 t - 1) (t^{3} - 8 t^{2} + 12) + (3 t^{2} - 16 t) (4 t^{2} - t)

Vereinfache

(8 t - 1) (t^{3} - 8 t^{2} + 12) + (3 t^{2} - 16 t) (4 t^{2} - t) : 20 t^{4} - 132 t^{3} + 24 t^{2} + 96 t - 12

= 20 t^{4} - 132 t^{3} + 24 t^{2} + 96 t - 12

x \to π - lim (\frac{x}{cos ( x ) + 1})

\int \frac{1}{z} d z

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