What is e^{-4t}(cos(4t)+4sin(4t)) ?

The solution to e^{-4t}(cos(4t)+4sin(4t)) is (cos(4t)+4sin(4t))/(e^{4t)}

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simplify e^{-4t}(cos(4t)+4sin(4t))

simplify

e^{- 4 t} (cos (4 t) + 4 sin (4 t))

\frac{cos ( 4 t ) + 4 sin ( 4 t )}{e ^{4 t}}

Solution steps

e^{- 4 t} (cos (4 t) + 4 sin (4 t))

Apply exponent rule:

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

= \frac{1}{e ^{4 t}} (cos (4 t) + 4 sin (4 t))

Multiply fractions:

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

= \frac{1 \cdot ( cos ( 4 t ) + 4 sin ( 4 t ) )}{e ^{4 t}}

1 \cdot (cos (4 t) + 4 sin (4 t)) = cos (4 t) + 4 sin (4 t)

= \frac{cos ( 4 t ) + 4 sin ( 4 t )}{e ^{4 t}}

1.9 \cdot 1 0^{- 3}

(8 y - 2 y^{2}) (8 y - 2 y^{2})

e^{- 0.13}

4 \cdot π \cdot 4^{2}

e^{- k t}

What is e^{-4t}(cos(4t)+4sin(4t)) ?
The solution to e^{-4t}(cos(4t)+4sin(4t)) is (cos(4t)+4sin(4t))/(e^{4t)}