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Beliebt Rechnen >

derivative f(x)=x^2(5x-1)^3

Lösung

ableitung von

f (x) = x^{2} (5 x - 1)^{3}

Lösung

2 x (5 x - 1)^{3} + 15 (5 x - 1)^{2} x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (5 x - 1)^{3})

Wende die Produktregel an:

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

f = x^{2}, g = (5 x - 1)^{3}

= \frac{d}{d x} (x^{2}) (5 x - 1)^{3} + \frac{d}{d x} ((5 x - 1)^{3}) x^{2}

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

\frac{d}{d x} ((5 x - 1)^{3}) = 15 (5 x - 1)^{2}

= 2 x (5 x - 1)^{3} + 15 (5 x - 1)^{2} x^{2}

Graph

Beliebte Beispiele

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