derivative 9x(2x^2+1)

解

導関数

9 x (2 x^{2} + 1)

9 (6 x^{2} + 1)

解答ステップ

\frac{d}{d x} (9 x (2 x^{2} + 1))

定数を除去:

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

= 9 \frac{d}{d x} (x (2 x^{2} + 1))

積の法則を適用:

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

f = x, g = 2 x^{2} + 1

= 9 (\frac{d x}{d x} (2 x^{2} + 1) + \frac{d}{d x} (2 x^{2} + 1) x)

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

簡素化

9 (1 \cdot (2 x^{2} + 1) + 4 xx) : 9 (6 x^{2} + 1)

= 9 (6 x^{2} + 1)