derivative of (3x^4-1(x-1))

Lösung

\frac{d}{d x} ((3 x^{4} - 1) (x - 1))

15 x^{4} - 12 x^{3} - 1

Schritte zur Lösung

\frac{d}{d x} ((3 x^{4} - 1) (x - 1))

Wende die Produktregel an:

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

f = 3 x^{4} - 1, g = x - 1

= \frac{d}{d x} (3 x^{4} - 1) (x - 1) + \frac{d}{d x} (x - 1) (3 x^{4} - 1)

\frac{d}{d x} (3 x^{4} - 1) = 12 x^{3}

\frac{d}{d x} (x - 1) = 1

= 12 x^{3} (x - 1) + 1 \cdot (3 x^{4} - 1)

Vereinfache

12 x^{3} (x - 1) + 1 \cdot (3 x^{4} - 1) : 15 x^{4} - 12 x^{3} - 1

= 15 x^{4} - 12 x^{3} - 1

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