derivative y=-8xln(6x+5)

解

導関数

y = - 8 x ln (6 x + 5)

- 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})

解答ステップ

\frac{d}{d x} (- 8 x ln (6 x + 5))

定数を除去:

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

= - 8 \frac{d}{d x} (x ln (6 x + 5))

積の法則を適用:

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

f = x, g = ln (6 x + 5)

= - 8 (\frac{d x}{d x} ln (6 x + 5) + \frac{d}{d x} (ln (6 x + 5)) x)

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

\frac{d}{d x} (ln (6 x + 5)) = \frac{6}{6 x + 5}

= - 8 (1 \cdot ln (6 x + 5) + \frac{6}{6 x + 5} x)

簡素化

- 8 (1 \cdot ln (6 x + 5) + \frac{6}{6 x + 5} x) : - 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})

= - 8 (ln (6 x + 5) + \frac{6 x}{6 x + 5})