derivative of axcos(x)

解

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

a (cos (x) - x sin (x))

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = x, g = cos (x)

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

\frac{d x}{d x} = 1

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

= a (1 \cdot cos (x) + (- sin (x)) x)

簡素化

= a (cos (x) - x sin (x))