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

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

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simplify e^t(cos(t)-sin(t))*2e^tcos(t)

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Add similar elements:

t + t = 2 t

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

(0.08 \cdot 5) (0.008 \cdot 5^{2} + 1)^{2} \cdot 5

(3.98 \cdot 1 0^{- 8}) \cdot \frac{1}{5.6}

6.421 \cdot 1 0^{- 5}

(10 - \frac{1}{2} e^{x}) \cdot (10 - \frac{1}{2} e^{x})

- lo g_{10} (3.2) 1 0^{- 4}

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