derivative arcsec(5x)

解

導関数

arcsec (5 x)

\frac{1}{x ^{2} 25 x ^{2} - 1}

解答ステップ

\frac{d}{d x} (arcsec (5 x))

連鎖法則を適用:

\frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \frac{d}{d x} (5 x)

= \frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

= \frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \cdot 5

簡素化

\frac{1}{( 5 x ) ^{2} ( 5 x ) ^{2} - 1} \cdot 5 : \frac{1}{x ^{2} 25 x ^{2} - 1}

= \frac{1}{x ^{2} 25 x ^{2} - 1}