簡約 e^{-t}*(cos(at))/t

解

簡約

e^{- t} \cdot \frac{cos ( a t )}{t}

\frac{cos ( t a )}{e ^{t} t}

解答ステップ

e^{- t} \frac{cos ( a t )}{t}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{cos ( t a )}{t} \cdot \frac{1}{e ^{t}}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot cos ( a t )}{e ^{t} t}

乗算:

1 \cdot cos (a t) = cos (a t)

= \frac{cos ( t a )}{e ^{t} t}