d/(dt)((sec^2(t))/(cos(t)(sec(t))))

解

\frac{d}{d t} (\frac{sec ^{2} ( t )}{cos ( t ) ( sec ( t ) )})

2 sec^{2} (t) tan (t)

解答ステップ

\frac{d}{d t} (\frac{sec ^{2} ( t )}{cos ( t ) ( sec ( t ) )})

簡素化

\frac{sec ^{2} ( t )}{cos ( t ) ( sec ( t ) )} : sec^{2} (t)

= \frac{d}{d t} (sec^{2} (t))

連鎖法則を適用:

2 sec (t) \frac{d}{d t} (sec (t))

= 2 sec (t) \frac{d}{d t} (sec (t))

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

= 2 sec (t) sec (t) tan (t)

簡素化

2 sec (t) sec (t) tan (t) : 2 sec^{2} (t) tan (t)

= 2 sec^{2} (t) tan (t)