derivative (arccot(x))^5

解

導関数

(arccot (x))^{5}

- \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

解答ステップ

\frac{d}{d x} ((arccot (x))^{5})

連鎖法則を適用:

5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

= 5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

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

= 5 (arccot (x))^{4} (- \frac{1}{x ^{2} + 1})

簡素化

5 arccot^{4} (x) (- \frac{1}{x ^{2} + 1}) : - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

= - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}