(d^2)/(dt^2)((x)(8-4t+t^2))

解

\frac{d ^{2}}{d t ^{2}} ((x) (8 - 4 t + t^{2}))

\frac{d ^{2} x}{d t ^{2}} (8 - 4 t + t^{2}) + 2 \frac{d x}{d t} (2 t - 4) + 2 x

解答ステップ

\frac{d ^{2}}{d t ^{2}} ((x) (8 - 4 t + t^{2}))

\frac{d}{d t} (x (8 - 4 t + t^{2})) = \frac{d x}{d t} (8 - 4 t + t^{2}) + (2 t - 4) x

= \frac{d}{d t} (\frac{d x}{d t} (8 - 4 t + t^{2}) + (2 t - 4) x)

\frac{d}{d t} (\frac{d x}{d t} (8 - 4 t + t^{2}) + (2 t - 4) x) = \frac{d ^{2} x}{d t ^{2}} (8 - 4 t + t^{2}) + 2 \frac{d x}{d t} (2 t - 4) + 2 x

= \frac{d ^{2} x}{d t ^{2}} (8 - 4 t + t^{2}) + 2 \frac{d x}{d t} (2 t - 4) + 2 x