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Beliebt Rechnen >

derivative (3x^2-3x+1)(x^3)

Lösung

ableitung von

(3 x^{2} - 3 x + 1) (x^{3})

Lösung

15 x^{4} - 12 x^{3} + 3 x^{2}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 3 x + 1) x^{3})

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (3 x^{2} - 3 x + 1) = 6 x - 3

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

= (6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1)

Vereinfache

(6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1) : 15 x^{4} - 12 x^{3} + 3 x^{2}

= 15 x^{4} - 12 x^{3} + 3 x^{2}

Graph

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