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Beliebt Rechnen >

derivative f(x)=x(x-4)^3

Lösung

ableitung von

f (x) = x (x - 4)^{3}

Lösung

(x - 4)^{3} + 3 x (x - 4)^{2}

Schritte zur Lösung

\frac{d}{d x} (x (x - 4)^{3})

Wende die Produktregel an:

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

f = x, g = (x - 4)^{3}

= \frac{d x}{d x} (x - 4)^{3} + \frac{d}{d x} ((x - 4)^{3}) x

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

\frac{d}{d x} ((x - 4)^{3}) = 3 (x - 4)^{2}

= 1 \cdot (x - 4)^{3} + 3 (x - 4)^{2} x

Vereinfache

= (x - 4)^{3} + 3 x (x - 4)^{2}

Graph

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