展开 (e^t)(e^{-t}-te^{-t})

解答

展开

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

1 - t

求解步骤

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

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

使用分配律:

a (b - c) = ab - a c

a = (e^{t}), b = e^{- t}, c = t e^{- t}

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

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

化简

e^{- t} (e^{t}) - e^{- t} t (e^{t}) : 1 - t

= 1 - t

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