What is cos(t)e^t*(-2)e^tsin(t) ?

The solution to cos(t)e^t*(-2)e^tsin(t) is -2e^{2t}cos(t)sin(t)

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simplify cos(t)e^t*(-2)e^tsin(t)

simplify

cos (t) e^{t} \cdot (- 2) e^{t} sin (t)

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

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{t} e^{t} = e^{t + t}

= cos (t) (- 2) e^{t + t} sin (t)

Add similar elements:

t + t = 2 t

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

Remove parentheses:

(- a) = - a

= - cos (t) \cdot 2 e^{2 t} sin (t)

e^{- 0.5 \cdot 4}

0.22 \cdot 1 0^{- 6}

\frac{x - 1}{x - 2}

x^{2} e^{- s x}

What is cos(t)e^t*(-2)e^tsin(t) ?
The solution to cos(t)e^t*(-2)e^tsin(t) is -2e^{2t}cos(t)sin(t)