What is e^{-st}(4t^2-5sin(3t)) ?

The solution to e^{-st}(4t^2-5sin(3t)) is (4t^2-5sin(3t))/(e^{st)}

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simplify e^{-st}(4t^2-5sin(3t))

simplify

e^{- s t} (4 t^{2} - 5 sin (3 t))

\frac{4 t ^{2} - 5 sin ( 3 t )}{e ^{s t}}

Solution steps

e^{- s t} (4 t^{2} - 5 sin (3 t))

Apply exponent rule:

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

= \frac{1}{e ^{s t}} (4 t^{2} - 5 sin (3 t))

Multiply fractions:

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

= \frac{1 \cdot ( 4 t ^{2} - 5 sin ( 3 t ) )}{e ^{s t}}

1 \cdot (4 t^{2} - 5 sin (3 t)) = 4 t^{2} - 5 sin (3 t)

= \frac{4 t ^{2} - 5 sin ( 3 t )}{e ^{s t}}

- 232

2^{t} e^{- r t}

0.5 x^{2} (\frac{1}{9} x^{3} - 1)^{- \frac{1}{2}}

4.2 \cdot 1 0^{- 5} (1 + 3 \cdot 1 0^{- 4} (170 - 20))

What is e^{-st}(4t^2-5sin(3t)) ?
The solution to e^{-st}(4t^2-5sin(3t)) is (4t^2-5sin(3t))/(e^{st)}