展开 A(e^{6t-3e^t}+e^{6t-3e^t}t(6-3e^t))

解答

展开

A (e^{6 t - 3 e^{t}} + e^{6 t - 3 e^{t}} t (6 - 3 e^{t}))

A e^{6 t - 3 e^{t}} + 6 A e^{6 t - 3 e^{t}} t - 3 A e^{7 t - 3 e^{t}} t

求解步骤

A (e^{6 t - 3 e^{t}} + e^{6 t - 3 e^{t}} t (6 - 3 e^{t}))

使用分配律:

a (b + c) = ab + a c

a = A, b = e^{6 t - 3 e^{t}}, c = e^{6 t - 3 e^{t}} t (6 - 3 e^{t})

= A e^{6 t - 3 e^{t}} + A e^{6 t - 3 e^{t}} t (6 - 3 e^{t})

乘开

A e^{6 t - 3 e^{t}} t (6 - 3 e^{t}) : 6 A e^{6 t - 3 e^{t}} t - 3 A e^{7 t - 3 e^{t}} t

= A e^{6 t - 3 e^{t}} + 6 A e^{6 t - 3 e^{t}} t - 3 A e^{7 t - 3 e^{t}} t

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