What is e^{-at}*sin(e^{-bt}*t) ?

The solution to e^{-at}*sin(e^{-bt}*t) is (sin(e^{-bt}t))/(e^{at)}

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simplify e^{-at}sin(e^{-bt}t)

simplify

e^{- a t} \cdot sin (e^{- b t} \cdot t)

\frac{sin ( e ^{- b t} t )}{e ^{a t}}

Solution steps

e^{- a t} sin (e^{- b t} t)

Apply exponent rule:

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

= \frac{1}{e ^{a t}} sin (e^{- b t} t)

Multiply fractions:

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

= \frac{1 \cdot sin ( e ^{- b t} t )}{e ^{a t}}

Multiply:

1 \cdot sin (e^{- b t} t) = sin (e^{- b t} t)

= \frac{sin ( e ^{- b t} t )}{e ^{a t}}

e^{6 θ}

(3 \cdot 1 0^{9}) \cdot (2 \cdot 1 0^{17})

\frac{- 30}{3}

(4 x^{3} y^{5}) (6 x^{5} y^{3})

What is e^{-at}*sin(e^{-bt}*t) ?
The solution to e^{-at}*sin(e^{-bt}*t) is (sin(e^{-bt}t))/(e^{at)}