derivative f(x)=(x+9)(x^2-9)

Lösung

ableitung von

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

3 x^{2} + 18 x - 9

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x + 9) = 1

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

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

Vereinfache

1 \cdot (x^{2} - 9) + 2 x (x + 9) : 3 x^{2} + 18 x - 9

= 3 x^{2} + 18 x - 9

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