derivative of ln((x^2+1/x))

解

\frac{d}{d x} (ln (\frac{x ^{2} + 1}{x}))

\frac{x ^{2} - 1}{x ( x ^{2} + 1 )}

解答ステップ

\frac{d}{d x} (ln (\frac{x ^{2} + 1}{x}))

連鎖法則を適用:

\frac{1}{\frac{x ^{2} + 1}{x}} \frac{d}{d x} (\frac{x ^{2} + 1}{x})

= \frac{1}{\frac{x ^{2} + 1}{x}} \frac{d}{d x} (\frac{x ^{2} + 1}{x})

\frac{d}{d x} (\frac{x ^{2} + 1}{x}) = \frac{x ^{2} - 1}{x ^{2}}

= \frac{1}{\frac{x ^{2} + 1}{x}} \cdot \frac{x ^{2} - 1}{x ^{2}}

簡素化

\frac{1}{\frac{x ^{2} + 1}{x}} \cdot \frac{x ^{2} - 1}{x ^{2}} : \frac{x ^{2} - 1}{x ( x ^{2} + 1 )}

= \frac{x ^{2} - 1}{x ( x ^{2} + 1 )}