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

解

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

\frac{1}{∣ x ∣}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{1}{∣ x ∣}