derivative h=t^2(6t-4)^3

Lösung

ableitung von

h (t) = t^{2} (6 t - 4)^{3}

2 t (6 t - 4)^{3} + 18 (6 t - 4)^{2} t^{2}

Schritte zur Lösung

\frac{d}{d t} (t^{2} (6 t - 4)^{3})

Wende die Produktregel an:

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

f = t^{2}, g = (6 t - 4)^{3}

= \frac{d}{d t} (t^{2}) (6 t - 4)^{3} + \frac{d}{d t} ((6 t - 4)^{3}) t^{2}

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

\frac{d}{d t} ((6 t - 4)^{3}) = 18 (6 t - 4)^{2}

= 2 t (6 t - 4)^{3} + 18 (6 t - 4)^{2} t^{2}

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