(\partial)/(\partial t)(4e^{sin(x+3ct)})

解答

\frac{\partial}{\partial t} (4 e^{s i n (x + 3 c t)})

12 c e^{s i n (x + 3 c t)} cos (x + 3 c t)

求解步骤

\frac{\partial}{\partial t} (4 e^{s i n (x + 3 c t)})

将

c, x

视为常数

将常数提出:

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

= 4 \frac{\partial}{\partial t} (e^{s i n (x + 3 c t)})

使用连锁律:

e^{s i n (x + 3 c t)} \frac{\partial}{\partial t} (sin (x + 3 c t))

= e^{s i n (x + 3 c t)} \frac{\partial}{\partial t} (sin (x + 3 c t))

\frac{\partial}{\partial t} (sin (x + 3 c t)) = cos (x + 3 c t) \cdot 3 c

= 4 e^{s i n (x + 3 c t)} cos (x + 3 c t) \cdot 3 c

化简

= 12 c e^{s i n (x + 3 c t)} cos (x + 3 c t)

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