derivative of 1/(tan^2(x))

解

\frac{d}{d x} (\frac{1}{tan ^{2} ( x )})

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

解答ステップ

\frac{d}{d x} (\frac{1}{tan ^{2} ( x )})

簡素化

\frac{1}{tan ^{2} ( x )} : cot^{2} (x)

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

連鎖法則を適用:

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

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

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

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

簡素化

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