derivative of 3(2cos(x-xsin(x)))

解

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

3 (- 3 sin (x) - x cos (x))

解答ステップ

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

定数を除去:

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

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

和/差の法則を適用:

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

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

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

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

= 3 (- 2 sin (x) - (sin (x) + x cos (x)))

簡素化

= 3 (- 3 sin (x) - x cos (x))