derivative x^2(x^3-1)

解

導関数

x^{2} (x^{3} - 1)

5 x^{4} - 2 x

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

= 5 x^{4} - 2 x