d/(d{x)}(({f}(x))(ln({x}{y})))

解

\frac{d}{d x} ((f (x)) (ln (x y)))

\frac{f ( x )}{x}

解答ステップ

\frac{d}{d x} ((f (x)) (ln (x y)))

定数を除去:

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

= f (x) \frac{d}{d x} (ln (x y))

連鎖法則を適用:

\frac{1}{x y} \frac{d}{d x} (x y)

= \frac{1}{x y} \frac{d}{d x} (x y)

\frac{d}{d x} (x y) = y

= f (x) \frac{1}{x y} y

簡素化

f (x) \frac{1}{x y} y : \frac{f ( x )}{x}

= \frac{f ( x )}{x}