What is te^{-t}sin(2tu(t)) ?

The solution to te^{-t}sin(2tu(t)) is (tsin(2t^2u))/(e^t)

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simplify te^{-t}sin(2tu(t))

simplify

t e^{- t} sin (2 t u (t))

\frac{t sin ( 2 t ^{2} u )}{e ^{t}}

Solution steps

t e^{- t} sin (2 t u (t))

Apply exponent rule:

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

= \frac{1}{e ^{t}} t sin (2 tt u)

Simplify

2 t u t : 2 t^{2} u

= \frac{1}{e ^{t}} t sin (2 t^{2} u)

Multiply fractions:

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

= \frac{1 \cdot t sin ( 2 u t ^{2} )}{e ^{t}}

Multiply:

1 \cdot t = t

= \frac{t sin ( 2 t ^{2} u )}{e ^{t}}

((1500 t + 1) e^{- 150 t}) (0.04 e^{- 150 t})

\frac{0.5 3 ^{2}}{0.8 8 ^{2}}

e^{- 1.7 x} \cdot - \frac{( 69 e ^{- \frac{69 x}{5}} )}{5}

3 (25 x^{2}) (3 y)

(1000) (1 \cdot 1 0^{- 3}) (9.81)

What is te^{-t}sin(2tu(t)) ?
The solution to te^{-t}sin(2tu(t)) is (tsin(2t^2u))/(e^t)