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

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

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

simplify

2 e^{- t} cos (3 t)

\frac{2 cos ( 3 t )}{e ^{t}}

Solution steps

2 e^{- t} cos (3 t)

Apply exponent rule:

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

= 2 \cdot \frac{1}{e ^{t}} cos (3 t)

Multiply fractions:

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

= \frac{1 \cdot 2 cos ( 3 t )}{e ^{t}}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 cos ( 3 t )}{e ^{t}}

3^{2 x} 5^{2 x} d x

3 - 5 \cdot 3 + 5

6 e^{- 0.12 x} cos (0.25 x)

(e^{- (\frac{x ^{2}}{5}) - (\frac{y ^{2}}{5})})^{2}

\frac{x ^{2}}{( 0.2 - x ) ^{2}}