derivative of sin(x-pi/6)

解

\frac{d}{d x} (sin (x - \frac{π}{6}))

\frac{3}{2} cos (x) + \frac{1}{2} sin (x)

解答ステップ

\frac{d}{d x} (sin (x - \frac{π}{6}))

簡素化

sin (x - \frac{π}{6}) : \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

= \frac{d}{d x} (\frac{3}{2} sin (x) - \frac{1}{2} cos (x))

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{3}{2} sin (x)) - \frac{d}{d x} (\frac{1}{2} cos (x))

\frac{d}{d x} (\frac{3}{2} sin (x)) = \frac{3}{2} cos (x)

\frac{d}{d x} (\frac{1}{2} cos (x)) = - \frac{1}{2} sin (x)

= \frac{3}{2} cos (x) - (- \frac{1}{2} sin (x))

簡素化

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)