What is e^{-2t}(3cos(6t)-5sin(6t)) ?

The solution to e^{-2t}(3cos(6t)-5sin(6t)) is (3cos(6t)-5sin(6t))/(e^{2t)}

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simplify e^{-2t}(3cos(6t)-5sin(6t))

simplify

e^{- 2 t} (3 cos (6 t) - 5 sin (6 t))

\frac{3 cos ( 6 t ) - 5 sin ( 6 t )}{e ^{2 t}}

Solution steps

e^{- 2 t} (3 cos (6 t) - 5 sin (6 t))

Apply exponent rule:

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

= \frac{1}{e ^{2 t}} (3 cos (6 t) - 5 sin (6 t))

Multiply fractions:

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

= \frac{1 \cdot ( 3 cos ( 6 t ) - 5 sin ( 6 t ) )}{e ^{2 t}}

1 \cdot (3 cos (6 t) - 5 sin (6 t)) = 3 cos (6 t) - 5 sin (6 t)

= \frac{3 cos ( 6 t ) - 5 sin ( 6 t )}{e ^{2 t}}

L t^{2} cosh (b) t

8.854 \cdot 1 0^{- 12}

(4 x^{6}) (6 x^{8})

5.401 \times 1 0^{- 1}

What is e^{-2t}(3cos(6t)-5sin(6t)) ?
The solution to e^{-2t}(3cos(6t)-5sin(6t)) is (3cos(6t)-5sin(6t))/(e^{2t)}