derivative 9x^3(x^2-2)

解

導関数

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

9 (5 x^{4} - 6 x^{2})

解答ステップ

\frac{d}{d x} (9 x^{3} (x^{2} - 2))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x^{3} (x^{2} - 2))

積の法則を適用:

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

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

= 9 (\frac{d}{d x} (x^{3}) (x^{2} - 2) + \frac{d}{d x} (x^{2} - 2) x^{3})

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

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

= 9 (3 x^{2} (x^{2} - 2) + 2 x x^{3})

簡素化

9 (3 x^{2} (x^{2} - 2) + 2 x x^{3}) : 9 (5 x^{4} - 6 x^{2})

= 9 (5 x^{4} - 6 x^{2})