derivative f(x)=x^3(x-4)^2

Lösung

ableitung von

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

5 x^{4} - 32 x^{3} + 48 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 4)^{2}

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

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

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

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

Vereinfache

3 x^{2} (x - 4)^{2} + 2 (x - 4) x^{3} : 5 x^{4} - 32 x^{3} + 48 x^{2}

= 5 x^{4} - 32 x^{3} + 48 x^{2}

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