derivative of x(x-21^2)

Lösung

\frac{d}{d x} (x (x - 21)^{2})

3 x^{2} - 84 x + 441

Schritte zur Lösung

\frac{d}{d x} (x (x - 21)^{2})

Wende die Produktregel an:

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

f = x, g = (x - 21)^{2}

= \frac{d x}{d x} (x - 21)^{2} + \frac{d}{d x} ((x - 21)^{2}) x

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

\frac{d}{d x} ((x - 21)^{2}) = 2 (x - 21)

= 1 \cdot (x - 21)^{2} + 2 (x - 21) x

Vereinfache

1 \cdot (x - 21)^{2} + 2 (x - 21) x : 3 x^{2} - 84 x + 441

= 3 x^{2} - 84 x + 441

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