derivative of 2arcsec(sqrt(x))

解

\frac{d}{d x} (2 arcsec (x))

\frac{1}{x x - 1}

解答ステップ

\frac{d}{d x} (2 arcsec (x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{1}{x x - 1}