derivative f(x)=4xsin(x)cos(x)

解

導関数

f (x) = 4 x sin (x) cos (x)

4 (sin (x) cos (x) + x cos (2 x))

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (sin (x) cos (x)) = cos (2 x)

= 4 (1 \cdot sin (x) cos (x) + cos (2 x) x)

簡素化

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