derivative 45+22sin((2pi)/(52)(t-10))

解

導関数

45 + 22 sin (\frac{2 π}{52} (t - 10))

\frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

解答ステップ

\frac{d}{d t} (45 + 22 sin (\frac{2 π}{52} (t - 10)))

簡素化

45 + 22 sin (\frac{2 π}{52} (t - 10)) : 45 + 22 sin (\frac{π ( t - 10 )}{26})

= \frac{d}{d t} (45 + 22 sin (\frac{π ( t - 10 )}{26}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (45) + \frac{d}{d t} (22 sin (\frac{π ( t - 10 )}{26}))

\frac{d}{d t} (45) = 0

\frac{d}{d t} (22 sin (\frac{π ( t - 10 )}{26})) = \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

= 0 + \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

簡素化

= \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})