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

解

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

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = x^{3}, g = ln (3 x - 2)

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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