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Beliebt Rechnen >

derivative (6x+5)(x^2-3x)

Lösung

ableitung von

(6 x + 5) (x^{2} - 3 x)

Lösung

18 x^{2} - 26 x - 15

Schritte zur Lösung

\frac{d}{d x} ((6 x + 5) (x^{2} - 3 x))

Wende die Produktregel an:

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

f = 6 x + 5, g = x^{2} - 3 x

= \frac{d}{d x} (6 x + 5) (x^{2} - 3 x) + \frac{d}{d x} (x^{2} - 3 x) (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

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

= 6 (x^{2} - 3 x) + (2 x - 3) (6 x + 5)

Vereinfache

6 (x^{2} - 3 x) + (2 x - 3) (6 x + 5) : 18 x^{2} - 26 x - 15

= 18 x^{2} - 26 x - 15

Graph

Beliebte Beispiele

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