d/(dt)((w)(5cos^2(t)-10sin^2(t)))

解

\frac{d}{d t} ((w) (5 cos^{2} (t) - 10 sin^{2} (t)))

- 30 w cos (t) sin (t)

解答ステップ

\frac{d}{d t} ((w) (5 cos^{2} (t) - 10 sin^{2} (t)))

w

を定数として扱う

定数を除去:

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

= w \frac{d}{d t} (5 cos^{2} (t) - 10 sin^{2} (t))

和/差の法則を適用:

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

= w (\frac{d}{d t} (5 cos^{2} (t)) - \frac{d}{d t} (10 sin^{2} (t)))

\frac{d}{d t} (5 cos^{2} (t)) = - 10 cos (t) sin (t)

\frac{d}{d t} (10 sin^{2} (t)) = 20 sin (t) cos (t)

= w (- 10 cos (t) sin (t) - 20 sin (t) cos (t))

簡素化

= - 30 w cos (t) sin (t)