d/(dt)((x)(12t^3))

解

\frac{d}{d t} ((x) (12 t^{3}))

12 (\frac{d x}{d t} t^{3} + 3 t^{2} x)

解答ステップ

\frac{d}{d t} ((x) (12 t^{3}))

定数を除去:

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

= 12 \frac{d}{d t} (x t^{3})

積の法則を適用:

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

f = x, g = t^{3}

= 12 (\frac{d x}{d t} t^{3} + \frac{d}{d t} (t^{3}) x)

\frac{d}{d t} (t^{3}) = 3 t^{2}

= 12 (\frac{d x}{d t} t^{3} + 3 t^{2} x)