derivative of arccot(sqrt(x))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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