d/(dt)(sin(t)cos(t))

解

\frac{d}{d t} (sin (t) cos (t))

cos (2 t)

解答ステップ

\frac{d}{d t} (sin (t) cos (t))

積の法則を適用:

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

f = sin (t), g = cos (t)

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

\frac{d}{d t} (sin (t)) = cos (t)

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

= cos (t) cos (t) + (- sin (t)) sin (t)

簡素化

cos (t) cos (t) + (- sin (t)) sin (t) : cos (2 t)

= cos (2 t)