(\partial)/(\partial t)((u(t,x))(3x-2t))

解

\frac{\partial}{\partial t} ((u (t, x)) (3 x - 2 t))

u ((, x \cdot 1) (3 x - 2 t) + (- 2) (t, x))

解答ステップ

\frac{\partial}{\partial t} ((u (t, x)) (3 x - 2 t))

u, x

を定数として扱う

定数を除去:

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

= u \frac{\partial}{\partial t} ((t, x) (3 x - 2 t))

積の法則を適用:

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

f = t, x, g = 3 x - 2 t

= u (\frac{\partial}{\partial t} (t, x) (3 x - 2 t) + \frac{\partial}{\partial t} (3 x - 2 t) (t, x))

\frac{\partial}{\partial t} (t, x) = (, x \cdot 1)

\frac{\partial}{\partial t} (3 x - 2 t) = - 2

= u ((, x \cdot 1) (3 x - 2 t) + (- 2) (t, x))