derivative of 25xsin(11x)

解

\frac{d}{d x} (25 x sin (11 x))

25 (sin (11 x) + 11 x cos (11 x))

解答ステップ

\frac{d}{d x} (25 x sin (11 x))

定数を除去:

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

= 25 \frac{d}{d x} (x sin (11 x))

積の法則を適用:

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

f = x, g = sin (11 x)

= 25 (\frac{d x}{d x} sin (11 x) + \frac{d}{d x} (sin (11 x)) x)

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

\frac{d}{d x} (sin (11 x)) = cos (11 x) \cdot 11

= 25 (1 \cdot sin (11 x) + cos (11 x) \cdot 11 x)

簡素化

= 25 (sin (11 x) + 11 x cos (11 x))