(\partial)/(\partial t)(tsin(t))

解

\frac{\partial}{\partial t} (t sin (t))

sin (t) + t cos (t)

解答ステップ

\frac{\partial}{\partial t} (t sin (t))

積の法則を適用:

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

f = t, g = sin (t)

= \frac{\partial}{\partial t} (t) sin (t) + \frac{\partial}{\partial t} (sin (t)) t

\frac{\partial}{\partial t} (t) = 1

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

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

簡素化

= sin (t) + t cos (t)