derivative f(x)=arccsc(3x)

解

導関数

f (x) = arccsc (3 x)

- \frac{1}{x ^{2} 9 x ^{2} - 1}

解答ステップ

\frac{d}{d x} (arccsc (3 x))

連鎖法則を適用:

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

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

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

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

簡素化

- \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3 : - \frac{1}{x ^{2} 9 x ^{2} - 1}

= - \frac{1}{x ^{2} 9 x ^{2} - 1}