derivative of x^3(x-4)

解

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

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

解答ステップ

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

積の法則を適用:

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

f = x^{3}, g = x - 4

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

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

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

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

簡素化

3 x^{2} (x - 4) + 1 \cdot x^{3} : 4 x^{3} - 12 x^{2}

= 4 x^{3} - 12 x^{2}