derivative y=arccsc(4x)

解

導関数

y = arccsc (4 x)

- \frac{1}{x ^{2} 16 x ^{2} - 1}

解答ステップ

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

連鎖法則を適用:

- \frac{1}{( 4 x ) ^{2} ( 4 x ) ^{2} - 1} \frac{d}{d x} (4 x)

= - \frac{1}{( 4 x ) ^{2} ( 4 x ) ^{2} - 1} \frac{d}{d x} (4 x)

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

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

簡素化

- \frac{1}{( 4 x ) ^{2} ( 4 x ) ^{2} - 1} \cdot 4 : - \frac{1}{x ^{2} 16 x ^{2} - 1}

= - \frac{1}{x ^{2} 16 x ^{2} - 1}