derivative of 5xln(3x)

解

\frac{d}{d x} (5 x ln (3 x))

5 (ln (3 x) + 1)

解答ステップ

\frac{d}{d x} (5 x ln (3 x))

定数を除去:

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

= 5 \frac{d}{d x} (x ln (3 x))

積の法則を適用:

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

f = x, g = ln (3 x)

= 5 (\frac{d x}{d x} ln (3 x) + \frac{d}{d x} (ln (3 x)) x)

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= 5 (1 \cdot ln (3 x) + \frac{1}{x} x)

簡素化

5 (1 \cdot ln (3 x) + \frac{1}{x} x) : 5 (ln (3 x) + 1)

= 5 (ln (3 x) + 1)