derivative of arccot(sqrt(x^2))

解

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

- \frac{x}{∣ x ∣ ( x ^{2} + 1 )}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{x}{∣ x ∣ ( x ^{2} + 1 )}