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Beliebt Rechnen >

derivative y=(6-x^2)(x^3-3x+4)

Lösung

ableitung von

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

Lösung

- 5 x^{4} + 27 x^{2} - 8 x - 18

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 6 - x^{2}, g = x^{3} - 3 x + 4

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

\frac{d}{d x} (6 - x^{2}) = - 2 x

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

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

Vereinfache

(- 2 x) (x^{3} - 3 x + 4) + (3 x^{2} - 3) (6 - x^{2}) : - 5 x^{4} + 27 x^{2} - 8 x - 18

= - 5 x^{4} + 27 x^{2} - 8 x - 18

Graph

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