derivative of x(12-2x^2)

Lösung

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

12 x^{2} - 96 x + 144

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (12 - 2 x)^{2}

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

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

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

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

Vereinfache

1 \cdot (12 - 2 x)^{2} + (- 4 (12 - 2 x)) x : 12 x^{2} - 96 x + 144

= 12 x^{2} - 96 x + 144

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