derivative of 2sin(pix-y)

解

\frac{d}{d x} (2 sin (π x - y))

2 cos (π x - y) (π - \frac{d y}{d x})

解答ステップ

\frac{d}{d x} (2 sin (π x - y))

定数を除去:

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

= 2 \frac{d}{d x} (sin (π x - y))

連鎖法則を適用:

cos (π x - y) \frac{d}{d x} (π x - y)

= cos (π x - y) \frac{d}{d x} (π x - y)

\frac{d}{d x} (π x - y) = π - \frac{d y}{d x}

= 2 cos (π x - y) (π - \frac{d y}{d x})