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Beliebt Rechnen >

derivative (8x^2+3x+1)*0.2x

Lösung

ableitung von

(8 x^{2} + 3 x + 1) \cdot 0.2 x

Lösung

0.2 (24 x^{2} + 6 x + 1)

Schritte zur Lösung

\frac{d}{d x} ((8 x^{2} + 3 x + 1) \cdot 0.2 x)

Entferne die Konstante:

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

= 0.2 \frac{d}{d x} ((8 x^{2} + 3 x + 1) x)

Wende die Produktregel an:

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

f = 8 x^{2} + 3 x + 1, g = x

= 0.2 (\frac{d}{d x} (8 x^{2} + 3 x + 1) x + \frac{d x}{d x} (8 x^{2} + 3 x + 1))

\frac{d}{d x} (8 x^{2} + 3 x + 1) = 16 x + 3

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

= 0.2 ((16 x + 3) x + 1 \cdot (8 x^{2} + 3 x + 1))

Vereinfache

0.2 ((16 x + 3) x + 1 \cdot (8 x^{2} + 3 x + 1)) : 0.2 (24 x^{2} + 6 x + 1)

= 0.2 (24 x^{2} + 6 x + 1)

Graph

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