derivative of 1/3 cos((6pix-1/2))

解

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

- π sin (\frac{6 π x - 1}{2})

解答ステップ

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

定数を除去:

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

= \frac{1}{3} \frac{d}{d x} (cos (\frac{6 π x - 1}{2}))

連鎖法則を適用:

- sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

= - sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

\frac{d}{d x} (\frac{6 π x - 1}{2}) = 3 π

= \frac{1}{3} (- sin (\frac{6 π x - 1}{2}) \cdot 3 π)

簡素化

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

= - π sin (\frac{6 π x - 1}{2})