derivative (2x-7)4(x^2+x+1)5

Lösung

ableitung von

(2 x - 7) 4 (x^{2} + x + 1) 5

20 (6 x^{2} - 10 x - 5)

Schritte zur Lösung

\frac{d}{d x} ((2 x - 7) \cdot 4 (x^{2} + x + 1) \cdot 5)

Vereinfache

(2 x - 7) \cdot 4 (x^{2} + x + 1) \cdot 5 : 20 (2 x - 7) (x^{2} + x + 1)

= \frac{d}{d x} (20 (2 x - 7) (x^{2} + x + 1))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 20 \frac{d}{d x} ((2 x - 7) (x^{2} + x + 1))

Wende die Produktregel an:

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

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

= 20 (\frac{d}{d x} (2 x - 7) (x^{2} + x + 1) + \frac{d}{d x} (x^{2} + x + 1) (2 x - 7))

\frac{d}{d x} (2 x - 7) = 2

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

= 20 (2 (x^{2} + x + 1) + (2 x + 1) (2 x - 7))

Multipliziere aus

2 (x^{2} + x + 1) + (2 x + 1) (2 x - 7) : 6 x^{2} - 10 x - 5

= 20 (6 x^{2} - 10 x - 5)

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