derivative of arccot(sqrt(x^2+1))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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