derivative of 3x^4-4x^3-12x^2+5

Lösung

\frac{d}{d x} (3 x^{4} - 4 x^{3} - 12 x^{2} + 5)

12 x^{3} - 12 x^{2} - 24 x

Schritte zur Lösung

\frac{d}{d x} (3 x^{4} - 4 x^{3} - 12 x^{2} + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (5)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (12 x^{2}) = 24 x

\frac{d}{d x} (5) = 0

= 12 x^{3} - 12 x^{2} - 24 x + 0

Vereinfache

= 12 x^{3} - 12 x^{2} - 24 x

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