d/(da)(tan(a)+cot(a))

解

\frac{d}{d a} (tan (a) + cot (a))

- 4 cot (2 a) csc (2 a)

解答ステップ

\frac{d}{d a} (tan (a) + cot (a))

簡素化

tan (a) + cot (a) : 2 csc (2 a)

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

定数を除去:

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

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

連鎖法則を適用:

- cot (2 a) csc (2 a) \frac{d}{d a} (2 a)

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

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

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

簡素化

= - 4 cot (2 a) csc (2 a)