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人気のある微分積分 >

derivative of xsin(6x)

解

\frac{d}{d x} (x sin (6 x))

解

sin (6 x) + 6 x cos (6 x)

解答ステップ

\frac{d}{d x} (x sin (6 x))

積の法則を適用:

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

f = x, g = sin (6 x)

= \frac{d x}{d x} sin (6 x) + \frac{d}{d x} (sin (6 x)) x

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

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= 1 \cdot sin (6 x) + cos (6 x) \cdot 6 x

簡素化

= sin (6 x) + 6 x cos (6 x)

グラフ

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