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

Lösung

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

- 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{4} + 3 x^{2}) = 4 x^{3} + 6 x

\frac{d}{d x} (1 - 5 x) = - 5

= (4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2})

Vereinfache

(4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2}) : - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

= - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

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