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Beliebt Rechnen >

derivative of (5x^3+3(x^4-2x))

Lösung

\frac{d}{d x} ((5 x^{3} + 3) (x^{4} - 2 x))

Lösung

35 x^{6} - 28 x^{3} - 6

Schritte zur Lösung

\frac{d}{d x} ((5 x^{3} + 3) (x^{4} - 2 x))

Wende die Produktregel an:

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

f = 5 x^{3} + 3, g = x^{4} - 2 x

= \frac{d}{d x} (5 x^{3} + 3) (x^{4} - 2 x) + \frac{d}{d x} (x^{4} - 2 x) (5 x^{3} + 3)

\frac{d}{d x} (5 x^{3} + 3) = 15 x^{2}

\frac{d}{d x} (x^{4} - 2 x) = 4 x^{3} - 2

= 15 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (5 x^{3} + 3)

Vereinfache

15 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (5 x^{3} + 3) : 35 x^{6} - 28 x^{3} - 6

= 35 x^{6} - 28 x^{3} - 6

Graph

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