derivative f(x)=x^6(x-1)^5

Lösung

ableitung von

f (x) = x^{6} (x - 1)^{5}

6 x^{5} (x - 1)^{5} + 5 (x - 1)^{4} x^{6}

Schritte zur Lösung

\frac{d}{d x} (x^{6} (x - 1)^{5})

Wende die Produktregel an:

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

f = x^{6}, g = (x - 1)^{5}

= \frac{d}{d x} (x^{6}) (x - 1)^{5} + \frac{d}{d x} ((x - 1)^{5}) x^{6}

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

\frac{d}{d x} ((x - 1)^{5}) = 5 (x - 1)^{4}

= 6 x^{5} (x - 1)^{5} + 5 (x - 1)^{4} x^{6}

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