derivative of 2/(sin^2(2x))

解

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

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

解答ステップ

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

簡素化

\frac{2}{sin ^{2} ( 2 x )} : 2 csc^{2} (2 x)

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

定数を除去:

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

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

簡素化

2 \cdot 2 csc (2 x) (- cot (2 x) csc (2 x) \cdot 2) : - 8 csc^{2} (2 x) cot (2 x)

= - 8 csc^{2} (2 x) cot (2 x)