(\partial)/(\partial x)(2ln(x)+ln(y))

解

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

\frac{2}{x}

解答ステップ

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

簡素化

2 ln (x) + ln (y) : ln (x^{2} y)

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

y

を定数として扱う

連鎖法則を適用:

\frac{1}{x ^{2} y} \frac{\partial}{\partial x} (x^{2} y)

= \frac{1}{x ^{2} y} \frac{\partial}{\partial x} (x^{2} y)

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

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

簡素化

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

= \frac{2}{x}