derivative of cos(2xy)

解

\frac{d}{d x} (cos (2 x) y)

- 2 sin (2 x) y + cos (2 x) \frac{d y}{d x}

解答ステップ

\frac{d}{d x} (cos (2 x) y)

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x), g = y

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

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

= (- sin (2 x) \cdot 2) y + \frac{d y}{d x} cos (2 x)

簡素化

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