derivative of csc^3(3-x)

解

\frac{d}{d x} (csc^{3} (3 - x))

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

解答ステップ

\frac{d}{d x} (csc^{3} (3 - x))

連鎖法則を適用:

3 (csc (3 - x))^{2} \frac{d}{d x} (csc (3 - x))

= 3 (csc (3 - x))^{2} \frac{d}{d x} (csc (3 - x))

\frac{d}{d x} (csc (3 - x)) = cot (3 - x) csc (3 - x)

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

簡素化

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

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