(\partial)/(\partial x)(ln(x^2u))

解

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

\frac{2}{x}

解答ステップ

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

u

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (x^{2} u) = 2 ux

= \frac{1}{x ^{2} u} \cdot 2 ux

簡素化

\frac{1}{x ^{2} u} \cdot 2 ux : \frac{2}{x}

= \frac{2}{x}