derivative y=cos((pit)/4-pi/3)

解

導関数

y = cos (\frac{π t}{4} - \frac{π}{3})

- \frac{π}{8} sin (\frac{π t}{4}) + \frac{3 π}{8} cos (\frac{π t}{4})

解答ステップ

\frac{d}{d t} (cos (\frac{π t}{4} - \frac{π}{3}))

簡素化

cos (\frac{π t}{4} - \frac{π}{3}) : \frac{1}{2} cos (\frac{π t}{4}) + \frac{3}{2} sin (\frac{π t}{4})

= \frac{d}{d t} (\frac{1}{2} cos (\frac{π t}{4}) + \frac{3}{2} sin (\frac{π t}{4}))

和/差の法則を適用:

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

= \frac{d}{d t} (\frac{1}{2} cos (\frac{π t}{4})) + \frac{d}{d t} (\frac{3}{2} sin (\frac{π t}{4}))

\frac{d}{d t} (\frac{1}{2} cos (\frac{π t}{4})) = - \frac{π}{8} sin (\frac{π t}{4})

\frac{d}{d t} (\frac{3}{2} sin (\frac{π t}{4})) = \frac{3 π}{8} cos (\frac{π t}{4})

= - \frac{π}{8} sin (\frac{π t}{4}) + \frac{3 π}{8} cos (\frac{π t}{4})