derivative of arccsc(2x+1)

解

\frac{d}{d x} (arccsc (2 x + 1))

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

解答ステップ

\frac{d}{d x} (arccsc (2 x + 1))

連鎖法則を適用:

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

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

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

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

簡素化

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

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