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Beliebt Rechnen >

derivative (x-9)(x-3)^2

Lösung

ableitung von

(x - 9) (x - 3)^{2}

Lösung

3 x^{2} - 30 x + 63

Schritte zur Lösung

\frac{d}{d x} ((x - 9) (x - 3)^{2})

Wende die Produktregel an:

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

f = x - 9, g = (x - 3)^{2}

= \frac{d}{d x} (x - 9) (x - 3)^{2} + \frac{d}{d x} ((x - 3)^{2}) (x - 9)

\frac{d}{d x} (x - 9) = 1

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

= 1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 9)

Vereinfache

1 \cdot (x - 3)^{2} + 2 (x - 3) (x - 9) : 3 x^{2} - 30 x + 63

= 3 x^{2} - 30 x + 63

Graph

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