What is e^{-6t}[acos(t)+dsin(t)] ?

The solution to e^{-6t}[acos(t)+dsin(t)] is (acos(t)+dsin(t))/(e^{6t)}

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simplify e^{-6t}[acos(t)+dsin(t)]

simplify

e^{- 6 t} [a cos (t) + d sin (t)]

\frac{a cos ( t ) + d sin ( t )}{e ^{6 t}}

Solution steps

e^{- 6 t} [a cos (t) + d sin (t)]

Apply exponent rule:

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

= \frac{1}{e ^{6 t}} [a cos (t) + d sin (t)]

Multiply fractions:

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

= \frac{1 \cdot ( a cos ( t ) + d sin ( t ) )}{e ^{6 t}}

1 \cdot (a cos (t) + d sin (t)) = a cos (t) + d sin (t)

= \frac{a cos ( t ) + d sin ( t )}{e ^{6 t}}

(2 - x) (1 - 3 x)^{- \frac{1}{2}}

- 6 e^{- 2 x}

0.25 \cdot 17.3 \cdot 1 0^{- 6} \cdot 190

[(\frac{5}{2})^{3}]^{- 4} \cdot (\frac{4}{5})^{- 2}

\frac{1}{3} e^{- 30}

What is e^{-6t}[acos(t)+dsin(t)] ?
The solution to e^{-6t}[acos(t)+dsin(t)] is (acos(t)+dsin(t))/(e^{6t)}