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Beliebt Rechnen >

derivative (x^2-12)(2x-9)

Lösung

ableitung von

(x^{2} - 12) (2 x - 9)

Lösung

6 x^{2} - 18 x - 24

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 12) (2 x - 9))

Wende die Produktregel an:

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

f = x^{2} - 12, g = 2 x - 9

= \frac{d}{d x} (x^{2} - 12) (2 x - 9) + \frac{d}{d x} (2 x - 9) (x^{2} - 12)

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

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

= 2 x (2 x - 9) + 2 (x^{2} - 12)

Vereinfache

2 x (2 x - 9) + 2 (x^{2} - 12) : 6 x^{2} - 18 x - 24

= 6 x^{2} - 18 x - 24

Graph

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