derivative of x^3(3x-8)

解

\frac{d}{d x} (x^{3} (3 x - 8))

12 x^{3} - 24 x^{2}

解答ステップ

\frac{d}{d x} (x^{3} (3 x - 8))

積の法則を適用:

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

f = x^{3}, g = 3 x - 8

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

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

\frac{d}{d x} (3 x - 8) = 3

= 3 x^{2} (3 x - 8) + 3 x^{3}

簡素化

3 x^{2} (3 x - 8) + 3 x^{3} : 12 x^{3} - 24 x^{2}

= 12 x^{3} - 24 x^{2}