d/(dt)((s)(3t^2-sec(t)+3))

解

\frac{d}{d t} ((s) (3 t^{2} - sec (t) + 3))

s (6 t - sec (t) tan (t))

解答ステップ

\frac{d}{d t} ((s) (3 t^{2} - sec (t) + 3))

定数を除去:

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

= s \frac{d}{d t} (3 t^{2} - sec (t) + 3)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= s (\frac{d}{d t} (3 t^{2}) - \frac{d}{d t} (sec (t)) + \frac{d}{d t} (3))

\frac{d}{d t} (3 t^{2}) = 6 t

\frac{d}{d t} (sec (t)) = sec (t) tan (t)

\frac{d}{d t} (3) = 0

= s (6 t - sec (t) tan (t) + 0)

簡素化

= s (6 t - sec (t) tan (t))