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Beliebt Rechnen >

derivative 5x^4(3x-7)

Lösung

ableitung von

5 x^{4} (3 x - 7)

Lösung

5 (15 x^{4} - 28 x^{3})

Schritte zur Lösung

\frac{d}{d x} (5 x^{4} (3 x - 7))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{4} (3 x - 7))

Wende die Produktregel an:

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

f = x^{4}, g = 3 x - 7

= 5 (\frac{d}{d x} (x^{4}) (3 x - 7) + \frac{d}{d x} (3 x - 7) x^{4})

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

\frac{d}{d x} (3 x - 7) = 3

= 5 (4 x^{3} (3 x - 7) + 3 x^{4})

Multipliziere aus

4 x^{3} (3 x - 7) + 3 x^{4} : 15 x^{4} - 28 x^{3}

= 5 (15 x^{4} - 28 x^{3})

Graph

Beliebte Beispiele

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