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Beliebt Rechnen >

derivative of x(3x^2-9)

Lösung

\frac{d}{d x} (x (3 x^{2} - 9))

Lösung

9 x^{2} - 9

Schritte zur Lösung

\frac{d}{d x} (x (3 x^{2} - 9))

Wende die Produktregel an:

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

f = x, g = 3 x^{2} - 9

= \frac{d x}{d x} (3 x^{2} - 9) + \frac{d}{d x} (3 x^{2} - 9) x

\frac{d x}{d x} = 1

\frac{d}{d x} (3 x^{2} - 9) = 6 x

= 1 \cdot (3 x^{2} - 9) + 6 xx

Vereinfache

1 \cdot (3 x^{2} - 9) + 6 xx : 9 x^{2} - 9

= 9 x^{2} - 9

Graph

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