derivative 2xln(3x-4)

解

導関数

2 x ln (3 x - 4)

2 (ln (3 x - 4) + \frac{3 x}{3 x - 4})

解答ステップ

\frac{d}{d x} (2 x ln (3 x - 4))

定数を除去:

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

= 2 \frac{d}{d x} (x ln (3 x - 4))

積の法則を適用:

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

f = x, g = ln (3 x - 4)

= 2 (\frac{d x}{d x} ln (3 x - 4) + \frac{d}{d x} (ln (3 x - 4)) x)

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

\frac{d}{d x} (ln (3 x - 4)) = \frac{3}{3 x - 4}

= 2 (1 \cdot ln (3 x - 4) + \frac{3}{3 x - 4} x)

簡素化

2 (1 \cdot ln (3 x - 4) + \frac{3}{3 x - 4} x) : 2 (ln (3 x - 4) + \frac{3 x}{3 x - 4})

= 2 (ln (3 x - 4) + \frac{3 x}{3 x - 4})