derivative of ln(x+sqrt(x^2+3))

解

\frac{d}{d x} (ln (x + x^{2} + 3))

\frac{1}{x ^{2} + 3}

解答ステップ

\frac{d}{d x} (ln (x + x^{2} + 3))

連鎖法則を適用:

\frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

= \frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

\frac{d}{d x} (x + x^{2} + 3) = 1 + \frac{x}{x ^{2} + 3}

= \frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3})

簡素化

\frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3}) : \frac{1}{x ^{2} + 3}

= \frac{1}{x ^{2} + 3}