derivative of ln(3x+5y)

解

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

\frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

解答ステップ

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

連鎖法則を適用:

\frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

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

= \frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x})

簡素化

\frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x}) : \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

= \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}