derivative of-4sin(xcos(x))

解

\frac{d}{d x} (- 4 sin (x) cos (x))

- 4 cos (2 x)

解答ステップ

\frac{d}{d x} (- 4 sin (x) cos (x))

簡素化

- 4 sin (x) cos (x) : - 2 sin (2 x)

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

定数を除去:

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

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

連鎖法則を適用:

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

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

\frac{d}{d x} (2 x) = 2

= - 2 cos (2 x) \cdot 2

簡素化

= - 4 cos (2 x)