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Beliebt Rechnen >

derivative f(x)=(3x-10)(2x^2-x+1)

Lösung

ableitung von

f (x) = (3 x - 10) (2 x^{2} - x + 1)

Lösung

18 x^{2} - 46 x + 13

Schritte zur Lösung

\frac{d}{d x} ((3 x - 10) (2 x^{2} - x + 1))

Wende die Produktregel an:

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

f = 3 x - 10, g = 2 x^{2} - x + 1

= \frac{d}{d x} (3 x - 10) (2 x^{2} - x + 1) + \frac{d}{d x} (2 x^{2} - x + 1) (3 x - 10)

\frac{d}{d x} (3 x - 10) = 3

\frac{d}{d x} (2 x^{2} - x + 1) = 4 x - 1

= 3 (2 x^{2} - x + 1) + (4 x - 1) (3 x - 10)

Vereinfache

3 (2 x^{2} - x + 1) + (4 x - 1) (3 x - 10) : 18 x^{2} - 46 x + 13

= 18 x^{2} - 46 x + 13

Graph

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