derivative of sin(xdx)

解

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

d (x cos (x) + sin (x))

解答ステップ

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

d

を定数として扱う

定数を除去:

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

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

積の法則を適用:

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

f = sin (x), g = x

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

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

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

= d (cos (x) x + 1 \cdot sin (x))

簡素化

= d (x cos (x) + sin (x))