derivative of (3x-1^5(2x+3)^4)

Lösung

\frac{d}{d x} ((3 x - 1)^{5} (2 x + 3)^{4})

15 (3 x - 1)^{4} (2 x + 3)^{4} + 8 (2 x + 3)^{3} (3 x - 1)^{5}

Schritte zur Lösung

\frac{d}{d x} ((3 x - 1)^{5} (2 x + 3)^{4})

Wende die Produktregel an:

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

f = (3 x - 1)^{5}, g = (2 x + 3)^{4}

= \frac{d}{d x} ((3 x - 1)^{5}) (2 x + 3)^{4} + \frac{d}{d x} ((2 x + 3)^{4}) (3 x - 1)^{5}

\frac{d}{d x} ((3 x - 1)^{5}) = 15 (3 x - 1)^{4}

\frac{d}{d x} ((2 x + 3)^{4}) = 8 (2 x + 3)^{3}

= 15 (3 x - 1)^{4} (2 x + 3)^{4} + 8 (2 x + 3)^{3} (3 x - 1)^{5}

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