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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

sin (t) sin (t) = sin^{1 + 1} (t)

= e^{t} (- 2) e^{t} sin^{1 + 1} (t)

Add the numbers:

1 + 1 = 2

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

Apply exponent rule:

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

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

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

Add similar elements:

t + t = 2 t

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

Remove parentheses:

(- a) = - a

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

(1 + e^{- x})^{- 1}

(F x + G) (x - 3) (5 x^{2}) (x^{2} + 25) (x^{2} + 1)^{2}

1200 e^{- 0.3}

1^{3} \cdot e^{- 3 \cdot 1}

\frac{( 1.5 ) ^{3}}{( 0.3 ) ^{3}}

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