d/(dt)((x)(5t^2+3t-7))

解

\frac{d}{d t} ((x) (5 t^{2} + 3 t - 7))

\frac{d x}{d t} (5 t^{2} + 3 t - 7) + (10 t + 3) x

解答ステップ

\frac{d}{d t} ((x) (5 t^{2} + 3 t - 7))

積の法則を適用:

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

f = x, g = 5 t^{2} + 3 t - 7

= \frac{d x}{d t} (5 t^{2} + 3 t - 7) + \frac{d}{d t} (5 t^{2} + 3 t - 7) x

\frac{d}{d t} (5 t^{2} + 3 t - 7) = 10 t + 3

= \frac{d x}{d t} (5 t^{2} + 3 t - 7) + (10 t + 3) x