(\partial)/(\partial y)(x^2ln(xy))

解

\frac{\partial}{\partial y} (x^{2} ln (x y))

\frac{x ^{2}}{y}

解答ステップ

\frac{\partial}{\partial y} (x^{2} ln (x y))

x

を定数として扱う

定数を除去:

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

= x^{2} \frac{\partial}{\partial y} (ln (x y))

連鎖法則を適用:

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

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

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

= x^{2} \frac{1}{x y} x

簡素化

x^{2} \frac{1}{x y} x : \frac{x ^{2}}{y}

= \frac{x ^{2}}{y}