derivative x(29-2x)(16-2x)

Lösung

ableitung von

x (29 - 2 x) (16 - 2 x)

12 x^{2} - 180 x + 464

Schritte zur Lösung

\frac{d}{d x} (x (29 - 2 x) (16 - 2 x))

Wende die Produktregel an:

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

f = x, g = (29 - 2 x) (16 - 2 x)

= \frac{d x}{d x} (29 - 2 x) (16 - 2 x) + \frac{d}{d x} ((29 - 2 x) (16 - 2 x)) x

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

\frac{d}{d x} ((29 - 2 x) (16 - 2 x)) = 8 x - 90

= 1 \cdot (29 - 2 x) (16 - 2 x) + (8 x - 90) x

Vereinfache

1 \cdot (29 - 2 x) (16 - 2 x) + (8 x - 90) x : 12 x^{2} - 180 x + 464

= 12 x^{2} - 180 x + 464

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