derivative y=csc(x)cot(x)

解

導関数

y = csc (x) cot (x)

csc (x) - 2 csc^{3} (x)

解答ステップ

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

積の法則を適用:

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

f = csc (x), g = cot (x)

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

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

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

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

簡素化

(- cot (x) csc (x)) cot (x) + (- csc^{2} (x)) csc (x) : csc (x) - 2 csc^{3} (x)

= csc (x) - 2 csc^{3} (x)