d/(d{y)}(ln({x}+2{y}+3{z}))

解

\frac{d}{d y} (ln (x + 2 y + 3 z))

\frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}

解答ステップ

\frac{d}{d y} (ln (x + 2 y + 3 z))

連鎖法則を適用:

\frac{1}{x + 2 y + 3 z} \frac{d}{d y} (x + 2 y + 3 z)

= \frac{1}{x + 2 y + 3 z} \frac{d}{d y} (x + 2 y + 3 z)

\frac{d}{d y} (x + 2 y + 3 z) = \frac{d}{d y} (x) + 2

= \frac{1}{x + 2 y + 3 z} (\frac{d}{d y} (x) + 2)

簡素化

\frac{1}{x + 2 y + 3 z} (\frac{d}{d y} (x) + 2) : \frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}

= \frac{\frac{d}{d y} ( x ) + 2}{x + 2 y + 3 z}