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

解答

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

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

求解步骤

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

将

u, x

视为常数

将常数提出:

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

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

使用微分乘法定则:

(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))

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e x p an d - \frac{12 ( 6 + 2 )}{17}

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