derivative 4x(x^2-9)

解

導関数

4 x (x^{2} - 9)

4 (3 x^{2} - 9)

解答ステップ

\frac{d}{d x} (4 x (x^{2} - 9))

定数を除去:

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

= 4 \frac{d}{d x} (x (x^{2} - 9))

積の法則を適用:

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

f = x, g = x^{2} - 9

= 4 (\frac{d x}{d x} (x^{2} - 9) + \frac{d}{d x} (x^{2} - 9) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot (x^{2} - 9) + 2 xx)

簡素化

4 (1 \cdot (x^{2} - 9) + 2 xx) : 4 (3 x^{2} - 9)

= 4 (3 x^{2} - 9)