derivative of ln(2+x^2)

解

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

\frac{2 x}{2 + x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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