derivative of 2csc^2(xcot(x))

解

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

4 csc^{2} (x) - 6 csc^{4} (x)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc^{2} (x), g = cot (x)

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

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

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

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

簡素化

2 ((- 2 csc^{2} (x) cot (x)) cot (x) + (- csc^{2} (x)) csc^{2} (x)) : 4 csc^{2} (x) - 6 csc^{4} (x)

= 4 csc^{2} (x) - 6 csc^{4} (x)