derivative of (2x+1^3(x-3)^4)

Lösung

\frac{d}{d x} ((2 x + 1)^{3} (x - 3)^{4})

6 (2 x + 1)^{2} (x - 3)^{4} + 4 (x - 3)^{3} (2 x + 1)^{3}

Schritte zur Lösung

\frac{d}{d x} ((2 x + 1)^{3} (x - 3)^{4})

Wende die Produktregel an:

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

f = (2 x + 1)^{3}, g = (x - 3)^{4}

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

\frac{d}{d x} ((2 x + 1)^{3}) = 6 (2 x + 1)^{2}

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

= 6 (2 x + 1)^{2} (x - 3)^{4} + 4 (x - 3)^{3} (2 x + 1)^{3}

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