derivative of (3x^5-1(2-x^4))

Lösung

\frac{d}{d x} ((3 x^{5} - 1) (2 - x^{4}))

30 x^{4} - 27 x^{8} + 4 x^{3}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{5} - 1) (2 - x^{4}))

Wende die Produktregel an:

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

f = 3 x^{5} - 1, g = 2 - x^{4}

= \frac{d}{d x} (3 x^{5} - 1) (2 - x^{4}) + \frac{d}{d x} (2 - x^{4}) (3 x^{5} - 1)

\frac{d}{d x} (3 x^{5} - 1) = 15 x^{4}

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

= 15 x^{4} (2 - x^{4}) + (- 4 x^{3}) (3 x^{5} - 1)

Vereinfache

15 x^{4} (2 - x^{4}) + (- 4 x^{3}) (3 x^{5} - 1) : 30 x^{4} - 27 x^{8} + 4 x^{3}

= 30 x^{4} - 27 x^{8} + 4 x^{3}

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