(\partial)/(\partial t)(te^{st})

解答

\frac{\partial}{\partial t} (t e^{s t})

e^{t s} + e^{t s} t s

求解步骤

\frac{\partial}{\partial t} (t e^{s t})

将

s

视为常数

使用微分乘法定则:

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

f = t, g = e^{s t}

= \frac{\partial}{\partial t} (t) e^{s t} + \frac{\partial}{\partial t} (e^{s t}) t

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

\frac{\partial}{\partial t} (e^{s t}) = e^{s t} s

= 1 \cdot e^{s t} + e^{s t} s t

化简

= e^{t s} + e^{t s} t s

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