What is 5(e^{-x}cos(1/2 x)) ?

The solution to 5(e^{-x}cos(1/2 x)) is (5cos(x/2))/(e^x)

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simplify 5(e^{-x}cos(1/2 x))

simplify

5 (e^{- x} cos (\frac{1}{2} x))

\frac{5 cos ( \frac{x}{2} )}{e ^{x}}

Solution steps

5 (e^{- x} cos (\frac{1}{2} x))

Apply exponent rule:

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

= 5 \cdot \frac{1}{e ^{x}} cos (\frac{1}{2} x)

Multiply

\frac{1}{2} x : \frac{x}{2}

= 5 \cdot \frac{1}{e ^{x}} cos (\frac{x}{2})

Multiply fractions:

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

= \frac{1 \cdot 5 cos ( \frac{x}{2} )}{e ^{x}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5 cos ( \frac{x}{2} )}{e ^{x}}

e^{- 9999999}

e^{- 0.0957}

(3 a) (4 a^{2})

x e^{- k x}

(3 x)^{3}

What is 5(e^{-x}cos(1/2 x)) ?
The solution to 5(e^{-x}cos(1/2 x)) is (5cos(x/2))/(e^x)