derivative (t+1)cos(-t)

解

導関数

(t + 1) cos (- t)

- sin (t) (1 + t) + cos (t)

解答ステップ

\frac{d}{d t} ((t + 1) cos (- t))

簡素化

(t + 1) cos (- t) : cos (t) (1 + t)

= \frac{d}{d t} (cos (t) (1 + t))

積の法則を適用:

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

f = cos (t), g = 1 + t

= \frac{d}{d t} (cos (t)) (1 + t) + \frac{d}{d t} (1 + t) cos (t)

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

\frac{d}{d t} (1 + t) = 1

= (- sin (t)) (1 + t) + 1 \cdot cos (t)

簡素化

= - sin (t) (1 + t) + cos (t)