d/(dt)((csc^2(t))/(-cot(t)(csc(t))))

解

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

- sec (t) tan (t)

解答ステップ

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

簡素化

\frac{csc ^{2} ( t )}{- cot ( t ) ( csc ( t ) )} : - sec (t)

= \frac{d}{d t} (- sec (t))

定数を除去:

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

= - \frac{d}{d t} (sec (t))

共通の導関数を適用:

\frac{d}{d t} (sec (t)) = sec (t) tan (t)

= - sec (t) tan (t)