derivative of arccsc(4x)

解答

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

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

求解步骤

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

使用连锁律:

- \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

化简

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

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