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

解

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

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

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

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

拡張

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

= 3 (5 x^{4} - 6 x^{2})