derivative of x(24-2x(24-2x))

Lösung

\frac{d}{d x} (x (24 - 2 x) (24 - 2 x))

12 x^{2} - 192 x + 576

Schritte zur Lösung

\frac{d}{d x} (x (24 - 2 x) (24 - 2 x))

Vereinfache

x (24 - 2 x) (24 - 2 x) : x (24 - 2 x)^{2}

= \frac{d}{d x} (x (24 - 2 x)^{2})

Wende die Produktregel an:

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

f = x, g = (24 - 2 x)^{2}

= \frac{d x}{d x} (24 - 2 x)^{2} + \frac{d}{d x} ((24 - 2 x)^{2}) x

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

\frac{d}{d x} ((24 - 2 x)^{2}) = - 4 (24 - 2 x)

= 1 \cdot (24 - 2 x)^{2} + (- 4 (24 - 2 x)) x

Vereinfache

1 \cdot (24 - 2 x)^{2} + (- 4 (24 - 2 x)) x : 12 x^{2} - 192 x + 576

= 12 x^{2} - 192 x + 576

x \to - 2 lim (\frac{5 x + 2}{x - 2})

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