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Beliebt Rechnen >

derivative x(2x-5)^3

Lösung

ableitung von

x (2 x - 5)^{3}

Lösung

(2 x - 5)^{3} + 6 x (2 x - 5)^{2}

Schritte zur Lösung

\frac{d}{d x} (x (2 x - 5)^{3})

Wende die Produktregel an:

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

f = x, g = (2 x - 5)^{3}

= \frac{d x}{d x} (2 x - 5)^{3} + \frac{d}{d x} ((2 x - 5)^{3}) x

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

\frac{d}{d x} ((2 x - 5)^{3}) = 6 (2 x - 5)^{2}

= 1 \cdot (2 x - 5)^{3} + 6 (2 x - 5)^{2} x

Vereinfache

= (2 x - 5)^{3} + 6 x (2 x - 5)^{2}

Graph

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