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Beliebt Rechnen >

derivative of x^2(20-x^3)

Lösung

\frac{d}{d x} (x^{2} (20 - x)^{3})

Lösung

2 x (20 - x)^{3} - 3 x^{2} (20 - x)^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (20 - x)^{3})

Wende die Produktregel an:

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

f = x^{2}, g = (20 - x)^{3}

= \frac{d}{d x} (x^{2}) (20 - x)^{3} + \frac{d}{d x} ((20 - x)^{3}) x^{2}

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

\frac{d}{d x} ((20 - x)^{3}) = - 3 (20 - x)^{2}

= 2 x (20 - x)^{3} + (- 3 (20 - x)^{2}) x^{2}

Vereinfache

= 2 x (20 - x)^{3} - 3 x^{2} (20 - x)^{2}

Graph

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