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Beliebt Rechnen >

derivative of x(4x-12^3)

Lösung

\frac{d}{d x} (x (4 x - 12)^{3})

Lösung

(4 x - 12)^{3} + 12 x (4 x - 12)^{2}

Schritte zur Lösung

\frac{d}{d x} (x (4 x - 12)^{3})

Wende die Produktregel an:

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

f = x, g = (4 x - 12)^{3}

= \frac{d x}{d x} (4 x - 12)^{3} + \frac{d}{d x} ((4 x - 12)^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((4 x - 12)^{3}) = 12 (4 x - 12)^{2}

= 1 \cdot (4 x - 12)^{3} + 12 (4 x - 12)^{2} x

Vereinfache

= (4 x - 12)^{3} + 12 x (4 x - 12)^{2}

Graph

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