derivative of 4(sin(x+xcos(x)))

解

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

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

解答ステップ

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

定数を除去:

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

= 4 \frac{d}{d x} (sin (x) + x cos (x))

和/差の法則を適用:

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

= 4 (\frac{d}{d x} (sin (x)) + \frac{d}{d x} (x cos (x)))

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

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

= 4 (cos (x) + cos (x) - x sin (x))

簡素化

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