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Beliebt Rechnen >

derivative f(x)=(x-2)(3-2x)(6-x)

Lösung

ableitung von

f (x) = (x - 2) (3 - 2 x) (6 - x)

Lösung

6 x^{2} - 38 x + 48

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x - 2, g = (3 - 2 x) (6 - x)

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

\frac{d}{d x} (x - 2) = 1

\frac{d}{d x} ((3 - 2 x) (6 - x)) = 4 x - 15

= 1 \cdot (3 - 2 x) (6 - x) + (4 x - 15) (x - 2)

Vereinfache

1 \cdot (3 - 2 x) (6 - x) + (4 x - 15) (x - 2) : 6 x^{2} - 38 x + 48

= 6 x^{2} - 38 x + 48

Graph

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