derivative-csc^2(x)

解

導関数

- csc^{2} (x)

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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