derivative csc^2(2x)

解

導関数

csc^{2} (2 x)

- 4 csc^{2} (2 x) cot (2 x)

解答ステップ

\frac{d}{d x} (csc^{2} (2 x))

連鎖法則を適用:

2 csc (2 x) \frac{d}{d x} (csc (2 x))

= 2 csc (2 x) \frac{d}{d x} (csc (2 x))

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= 2 csc (2 x) (- cot (2 x) csc (2 x) \cdot 2)

簡素化

2 csc (2 x) (- cot (2 x) csc (2 x) \cdot 2) : - 4 csc^{2} (2 x) cot (2 x)

= - 4 csc^{2} (2 x) cot (2 x)