derivative of tan(x-cot(x))

解

\frac{d}{d x} (tan (x) - cot (x))

4 csc^{2} (2 x)

解答ステップ

\frac{d}{d x} (tan (x) - cot (x))

簡素化

tan (x) - cot (x) : - 2 cot (2 x)

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= - 2 (- csc^{2} (2 x) \cdot 2)

簡素化

= 4 csc^{2} (2 x)