derivative of ar(xcos(x))

解

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

a (cos (x) \frac{d}{d x} (r (x)) - sin (x) r (x))

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = r (x), g = cos (x)

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

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

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

簡素化

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