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Beliebt Rechnen >

derivative of x(x-15^2)

Lösung

\frac{d}{d x} (x (x - 15)^{2})

Lösung

3 x^{2} - 60 x + 225

Schritte zur Lösung

\frac{d}{d x} (x (x - 15)^{2})

Wende die Produktregel an:

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

f = x, g = (x - 15)^{2}

= \frac{d x}{d x} (x - 15)^{2} + \frac{d}{d x} ((x - 15)^{2}) x

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

\frac{d}{d x} ((x - 15)^{2}) = 2 (x - 15)

= 1 \cdot (x - 15)^{2} + 2 (x - 15) x

Vereinfache

1 \cdot (x - 15)^{2} + 2 (x - 15) x : 3 x^{2} - 60 x + 225

= 3 x^{2} - 60 x + 225

Graph

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