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Beliebt Rechnen >

derivative f(x)=x(x^2+6)

Lösung

ableitung von

f (x) = x (x^{2} + 6)

Lösung

3 x^{2} + 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x^{2} + 6

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

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

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

= 1 \cdot (x^{2} + 6) + 2 xx

Vereinfache

1 \cdot (x^{2} + 6) + 2 xx : 3 x^{2} + 6

= 3 x^{2} + 6

Graph

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