展开 e^t(e^{-t}t-2e^{-t})

解答

展开

e^{t} (e^{- t} t - 2 e^{- t})

t - 2

求解步骤

e^{t} (e^{- t} t - 2 e^{- t})

使用分配律:

a (b - c) = ab - a c

a = e^{t}, b = e^{- t} t, c = 2 e^{- t}

= e^{t} e^{- t} t - e^{t} \cdot 2 e^{- t}

= e^{t} e^{- t} t - 2 e^{t} e^{- t}

化简

e^{t} e^{- t} t - 2 e^{t} e^{- t} : t - 2

= t - 2

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