derivative of csc^4(x)

解答

\frac{d}{d x} (csc^{4} (x))

- 4 csc^{4} (x) cot (x)

求解步骤

\frac{d}{d x} (csc^{4} (x))

使用连锁律:

4 (csc (x))^{3} \frac{d}{d x} (csc (x))

= 4 (csc (x))^{3} \frac{d}{d x} (csc (x))

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 4 (csc (x))^{3} (- cot (x) csc (x))

化简

4 csc^{3} (x) (- cot (x) csc (x)) : - 4 csc^{4} (x) cot (x)

= - 4 csc^{4} (x) cot (x)