derivative y=x^3(2x-1)^7

Lösung

ableitung von

y = x^{3} (2 x - 1)^{7}

3 x^{2} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{3}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (2 x - 1)^{7})

Wende die Produktregel an:

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

f = x^{3}, g = (2 x - 1)^{7}

= \frac{d}{d x} (x^{3}) (2 x - 1)^{7} + \frac{d}{d x} ((2 x - 1)^{7}) x^{3}

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

\frac{d}{d x} ((2 x - 1)^{7}) = 14 (2 x - 1)^{6}

= 3 x^{2} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{3}

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