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Beliebt Rechnen >

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

Lösung

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

Lösung

4 (2 x (3 x - 1)^{3} + 9 (3 x - 1)^{2} x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((3 x - 1)^{3}) = 9 (3 x - 1)^{2}

= 4 (2 x (3 x - 1)^{3} + 9 (3 x - 1)^{2} x^{2})

Graph

Beliebte Beispiele

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