derivative (7x+1)(x^2-6)

Lösung

ableitung von

(7 x + 1) (x^{2} - 6)

21 x^{2} + 2 x - 42

Schritte zur Lösung

\frac{d}{d x} ((7 x + 1) (x^{2} - 6))

Wende die Produktregel an:

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

f = 7 x + 1, g = x^{2} - 6

= \frac{d}{d x} (7 x + 1) (x^{2} - 6) + \frac{d}{d x} (x^{2} - 6) (7 x + 1)

\frac{d}{d x} (7 x + 1) = 7

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

= 7 (x^{2} - 6) + 2 x (7 x + 1)

Vereinfache

7 (x^{2} - 6) + 2 x (7 x + 1) : 21 x^{2} + 2 x - 42

= 21 x^{2} + 2 x - 42

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