d/(dt)(a_{2}tcos(2t)+a_{2}tsin(2t))

解

\frac{d}{d t} (a_{2} t cos (2 t) + a_{2} t sin (2 t))

a_{2} (cos (2 t) - 2 t sin (2 t)) + a_{2} (sin (2 t) + 2 t cos (2 t))

解答ステップ

\frac{d}{d t} (a_{2} t cos (2 t) + a_{2} t sin (2 t))

和/差の法則を適用:

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

= \frac{d}{d t} (a_{2} t cos (2 t)) + \frac{d}{d t} (a_{2} t sin (2 t))

\frac{d}{d t} (a_{2} t cos (2 t)) = a_{2} (cos (2 t) - 2 t sin (2 t))

\frac{d}{d t} (a_{2} t sin (2 t)) = a_{2} (sin (2 t) + 2 t cos (2 t))

= a_{2} (cos (2 t) - 2 t sin (2 t)) + a_{2} (sin (2 t) + 2 t cos (2 t))