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Beliebt Rechnen >

derivative of 3x^4-2x^3-12x^2+18x+15

Lösung

\frac{d}{d x} (3 x^{4} - 2 x^{3} - 12 x^{2} + 18 x + 15)

Lösung

12 x^{3} - 6 x^{2} - 24 x + 18

Schritte zur Lösung

\frac{d}{d x} (3 x^{4} - 2 x^{3} - 12 x^{2} + 18 x + 15)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (18 x) + \frac{d}{d x} (15)

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

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

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

\frac{d}{d x} (18 x) = 18

\frac{d}{d x} (15) = 0

= 12 x^{3} - 6 x^{2} - 24 x + 18 + 0

Vereinfache

= 12 x^{3} - 6 x^{2} - 24 x + 18

Graph

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