derivative arcsec(2x+3)

解

導関数

arcsec (2 x + 3)

\frac{1}{( 2 x + 3 ) ^{2} x ^{2} + 3 x + 2}

解答ステップ

\frac{d}{d x} (arcsec (2 x + 3))

連鎖法則を適用:

\frac{1}{( 2 x + 3 ) ^{2} ( 2 x + 3 ) ^{2} - 1} \frac{d}{d x} (2 x + 3)

= \frac{1}{( 2 x + 3 ) ^{2} ( 2 x + 3 ) ^{2} - 1} \frac{d}{d x} (2 x + 3)

\frac{d}{d x} (2 x + 3) = 2

= \frac{1}{( 2 x + 3 ) ^{2} ( 2 x + 3 ) ^{2} - 1} \cdot 2

簡素化

\frac{1}{( 2 x + 3 ) ^{2} ( 2 x + 3 ) ^{2} - 1} \cdot 2 : \frac{1}{( 2 x + 3 ) ^{2} x ^{2} + 3 x + 2}

= \frac{1}{( 2 x + 3 ) ^{2} x ^{2} + 3 x + 2}