What is e^tcos(t)e^tsin(t) ?

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

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simplify e^tcos(t)e^tsin(t)

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Add similar elements:

t + t = 2 t

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

(t + 1)^{2} (t - 1)^{2}

y \cdot y^{- \frac{1}{2}}

x - 3 \cdot x - 5

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