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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (1 - 3 x)^{2}, g = (x^{2} - 2)^{3}

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

\frac{d}{d x} ((1 - 3 x)^{2}) = - 6 (1 - 3 x)

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

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

Vereinfache

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

Graph

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