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Beliebt Rechnen >

derivative 6x^5(x^4-8)

Lösung

ableitung von

6 x^{5} (x^{4} - 8)

Lösung

6 (9 x^{8} - 40 x^{4})

Schritte zur Lösung

\frac{d}{d x} (6 x^{5} (x^{4} - 8))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{5} (x^{4} - 8))

Wende die Produktregel an:

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

f = x^{5}, g = x^{4} - 8

= 6 (\frac{d}{d x} (x^{5}) (x^{4} - 8) + \frac{d}{d x} (x^{4} - 8) x^{5})

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

\frac{d}{d x} (x^{4} - 8) = 4 x^{3}

= 6 (5 x^{4} (x^{4} - 8) + 4 x^{3} x^{5})

Vereinfache

6 (5 x^{4} (x^{4} - 8) + 4 x^{3} x^{5}) : 6 (9 x^{8} - 40 x^{4})

= 6 (9 x^{8} - 40 x^{4})

Graph

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