derivative of arccot(sqrt(4x))

解

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

- \frac{1}{x ( 4 x + 1 )}

解答ステップ

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

簡素化

arccot (4 x) : arccot (2 x)

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{1}{x ( 4 x + 1 )}