What is t(cos(sqrt(2t)))e^{-2t} ?

The solution to t(cos(sqrt(2t)))e^{-2t} is (tcos(sqrt(2)sqrt(t)))/(e^{2t)}

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simplify t(cos(sqrt(2t)))e^{-2t}

simplify

t (cos (2 t)) e^{- 2 t}

\frac{t cos ( 2 t )}{e ^{2 t}}

Solution steps

t (cos (2 t)) e^{- 2 t}

Apply exponent rule:

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

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

2 t = 2 t

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

Multiply fractions:

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

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

Multiply:

1 \cdot t = t

= \frac{t cos ( 2 t )}{e ^{2 t}}

e^{t} \cdot e^{3 x}

5.21 \cdot 1 0^{- 3}

60 e^{- 4.8 t} sin (16 t)

2.78 \cdot 1 0^{- 3}

- y \cdot e^{- y}

What is t(cos(sqrt(2t)))e^{-2t} ?
The solution to t(cos(sqrt(2t)))e^{-2t} is (tcos(sqrt(2)sqrt(t)))/(e^{2t)}